Journal articles on the topic 'Hydrodynamics – Mathematical models'
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1
Korobkin, Alexander, Emilian I. Părău, and Jean-Marc Vanden-Broeck. "The mathematical challenges and modelling of hydroelasticity." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1947 (July 28, 2011): 2803–12. http://dx.doi.org/10.1098/rsta.2011.0116.
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Hydroelasticity brings together hydrodynamics and elastic theories. It is concerned with deformations of elastic bodies responding to hydrodynamic excitations, which themselves depend on elastic deformation. This Theme Issue is intended to identify and to outline mathematical problems of modern hydroelasticity and to review recent developments in this area, including physically and mathematically elaborated models and the techniques used in their analysis.
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Paryshev, Emil V. "Approximate mathematical models in high-speed hydrodynamics." Journal of Engineering Mathematics 55, no. 1-4 (July 26, 2006): 41–64. http://dx.doi.org/10.1007/s10665-005-9026-x.
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Holdych, D. J., D. Rovas, J. G. Georgiadis, and R. O. Buckius. "An Improved Hydrodynamics Formulation for Multiphase Flow Lattice-Boltzmann Models." International Journal of Modern Physics C 09, no. 08 (December 1998): 1393–404. http://dx.doi.org/10.1142/s0129183198001266.
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Lattice-Boltzmann (LB) models provide a systematic formulation of effective-field computational approaches to the calculation of multiphase flow by replacing the mathematical surface of separation between the vapor and liquid with a thin transition region, across which all magnitudes change continuously. Many existing multiphase models of this sort do not satisfy the rigorous hydrodynamic constitutive laws. Here, we extend the two-dimensional, seven-speed Swift et al. LB model1 to rectangular grids (nine speeds) by using symbolic manipulation (MathematicaTM) and compare the LB model predictions with benchmark problems, in order to evaluate its merits. Particular emphasis is placed on the stress tensor formulation. Comparison with the two-phase analogue of the Couette flow and with a flow involving shear and advection of a droplet surrounded by its vapor reveals that additional terms have to be introduced in the definition of the stress tensor in order to satisfy the Navier–Stokes equation in regions of high density gradients. The use of Mathematica obviates many of the difficulties with the calculations "by-hand," allowing at the same time more flexibility to the computational analyst to experiment with geometrical and physical parameters of the formulation.
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Sukhinov, A., A. Chistyakov, S. Protsenko, and E. Protsenko. "Study of 3D discrete hydrodynamics models using cell filling." E3S Web of Conferences 224 (2020): 02016. http://dx.doi.org/10.1051/e3sconf/202022402016.
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Modern methods and tools for coastal hydrodynamics modeling indicate the necessity of constructing discrete analogs of models for ones the properties: balance and conservation laws (for mass, flows, impulse), stability, convergence and etc. have been fulfilled. The paper considers a continuous three-dimensional mathematical model of the hydrodynamics of water basins and its discretization. The pressure correction method at variable water medium density was used to solve the problem of hydrodynamics. The considered discrete mathematical models of hydrodynamics take into account the filling of control cells on rectangular grids. This increased the accuracy of the solution in the case of complex geometry by improving the boundary approximation. From the obtained estimates of the components of the velocity vector, it follows that there are no two or more stationary regimes in which all forces are balanced, and the solution to the discrete problem exists and is unique and tends to the solution of the continuous problem upon reaching the stationary regime. Also the balance of the flows for the discrete model has been proved as well as absence of non-conservative dissipative terms.
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Rahimi-Ahar, Zohreh, and Mohammad Sadegh Hatamipour. "Hydrodynamics, numerical study and application of spouted bed." Reviews in Chemical Engineering 34, no. 6 (November 27, 2018): 743–66. http://dx.doi.org/10.1515/revce-2017-0036.
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Abstract This article reviews the major research and development on spouted beds (SBs). Due to its unique structural and flow characteristics, the SB is a very successful system in most applications. Two-phase and sometimes three-phase interactions generate a large number of variables to be noted in each process. Up-to-date information on the fundamentals and applications of SBs has been briefly presented, based on the published works. Thousands of interesting studies on hydrodynamic characteristics, numerical simulations, and new applications of SBs are reported. In the first step, the present work presents a review of hydrodynamic characteristics (circulation of solids in SB, measurement techniques for particle tracking and empirical hydrodynamics, pressure drop, maximum spoutable height, minimum spouting velocity, and diameter of the spout). In the second step, main mathematical models and computational fluid dynamics (CFD) simulation of the SB to predict and analyze different processes are described. Some main mathematical modeling and the recent advances of two fluid methods and discrete element method approaches in CFD simulation of SBs are summarized. In the last step, some new applications of the SB are presented. As the result of this review, we can observe the importance of further development of hydrodynamics structure, working on modeling and related correlations and improve the applications of SBs.
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Li, Hui, and Hui Yang. "Numerical Investigation of Hydrodynamic Behaviors in Gas-Solid Magnetic Fluidized Beds." Advanced Materials Research 560-561 (August 2012): 1165–73. http://dx.doi.org/10.4028/www.scientific.net/amr.560-561.1165.
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A mathematical model describing the transient hydrodynamic behaviours is introduced to predict the effect of magnetic field intensity and process parameters in magnetically stable fluidized beds (MSFBs). Computational fluid dynamics (CFD) code Fluent 6.2 has been used to investigate the hydrodynamics of a gas-solid MSFB operated with fine particles. The model is incorporated into simulations based on an Eulerian approach. In the simulations, the closure models describing the hydrodynamics of the solids phase are directly affected by the behavior of magnetic field intensity. The simulations are compared with experiments at different gas Reynolds numbers (ReG = uGdp/vG) and magnetic field intensity (Er = 3μ0MpH/2gdpρp). The agreement obtained between the simulation results and experimental data for local solid holdup is good at lower ReG and Er values.
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Khvostov, Anatoly, Anatoly Khvostov, Viktor Ryazhskikh, Viktor Ryazhskikh, Gazibeg Magomedov, Gazibeg Magomedov, Aleksey Zhuravlev, and Aleksey Zhuravlev. "Matrix dynamic models of elements of technological systems with perfect mixing and plug-flow hydrodynamics in Simulink." Foods and Raw Materials 6, no. 2 (December 20, 2018): 483–92. http://dx.doi.org/10.21603/2308-4057-2018-2-483-492.
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The dynamic models of elements of technological systems with perfect mixing and plug-flow hydrodynamics are based on the systems of algebraic and differential equations that describe a change in the basic technological parameters. The main difficulty in using such models in MathWorks Simulink™ computer simulation systems is the representation of ordinary differential equations (ODE) and partial differential equations (PDE) that describe the dynamics of a process as a MathWorks Simulink™ block set. The study was aimed at developing an approach to the synthesis of matrix dynamic models of elements of technological systems with perfect mixing and plug-flow hydrodynamics that allows for transition from PDE to an ODE system on the basis of matrix representation of discretization of coordinate derivatives. A sugar syrup cooler was chosen as an object of modeling. The mathematical model of the cooler is formalized by a set of perfect reactors. The simulation results showed that the mathematical model adequately describes the main regularities of the process, the deviation of the calculated data from the regulations did not exceed 10%. The proposed approach significantly simplifies the study and modernization of the current and the development of new technological equipment, as well as the synthesis of algorithms for controlling the processes therein.
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Al-Isawi, J. K. T. "Computational Experiments for One Class of Mathematical Models in Thermodynamics and Hydrodynamics." Journal of Computational and Engineering Mathematics 4, no. 1 (2017): 16–26. http://dx.doi.org/10.14529/jcem170102.
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A. A., Yuldashov, and Karimov G. X. "Models of Distribution of Flow Parameters in Intensive Garden Irrigation, System Pipes." International Journal for Research in Applied Science and Engineering Technology 10, no. 3 (March 31, 2022): 838–44. http://dx.doi.org/10.22214/ijraset.2022.40692.
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Annotation: The mathematical description of the movement of water in the systems of irrigation pipelines, based on the equation of continuity of the medium, the system of Navy-Stokes equations. The resulting mathematical package describes a system with distributed parameters and is performed based on the condition of dynamic balance at the point of flow, taking into account the dependence on the nature of the flow and the physical properties of the environment. Calculation is executed with use of functions Besseliya. Methodology for calculating the hydrodynamic component of water movement in irrigation water supply systems. Pipelines are universal in nature and can be used in the calculation, construction and assessment of the stability of water supply hydraulic systems; the technique can be used to describe the object of operation in the construction of control systems for the hydraulic parameters of the water supply system. Keywords: pipeline, irrigation systems, non-uniformity, liquid, water, strength, function, three-dimensional, water supply, hydrodynamics, hydrostatics, quasi-one-dimensional, unsteady, flow, potential, surface, coordinate system, stresses, projection, velocity, cylindrical coordinates, unsteady motion , asymmetric, viscous, compressible fluid, plastic pipe
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Korniyenko, Bogdan, and Andrii Nesteruk. "Mathematical modelling of granulation process in fluidised bed (overview of models)." Proceedings of the NTUU “Igor Sikorsky KPI”. Series: Chemical engineering, ecology and resource saving, no. 2 (June 30, 2022): 51–59. http://dx.doi.org/10.20535/2617-9741.2.2022.260349.
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One of the most common methods of making mineral fertilizers is granulation. Fertilizers in the form of granules have a number of advantages over conventional fertilizers in the form of powder or liquid, namely, ease of transportation, well absorbed and less susceptible to weathering from the soil, convenient to use. To obtain solid particles from liquid starting material such as solutions, emulsions or suspensions, the following processes are used: crystallization, granulation, spray drying. Depending on the focus of the study, the fluidized bed granulation process can be modeled at different levels of abstraction. The dynamics of individual particles is modeled on a microscopic scale. The interaction of a particle with a liquid, equipment or other particles is considered. The next rougher level of abstraction is the mesoscale. Here the particles are divided into classes according to their characteristics. It is assumed that the particles of the class have the same properties and dynamics. On a macroscopic scale, the roughest level of approximation, attention is focused on the integral behavior of the whole set of particles. As a result, the selected characteristic values describe the state of the particle layer. There are different approaches to modeling for each scale. It is proposed to describe the microscopic scale using the hydrodynamics model, the mesoscale using the balance model, and the macroscopic scale using the moments method or the Lagrange-Euler model. A combined balance-hydrodynamics model and a multi-chamber balance model that can be used for the tasks of building information technology for fluidized bed granulation process control technology are also considered.
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Pomraning, G. C., and R. H. Szilard. "Flux-limited diffusion models in radiation hydrodynamics." Transport Theory and Statistical Physics 22, no. 2-3 (April 1993): 187–220. http://dx.doi.org/10.1080/00411459308203812.
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SAVVIDIS, Y. G., M. G. DODOU, Y. N. KRESTENITIS, and C. G. KOUTITAS. "Modeling of the upwelling hydrodynamics in the Aegean Sea." Mediterranean Marine Science 5, no. 1 (June 1, 2004): 5. http://dx.doi.org/10.12681/mms.205.
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The special features of the hydrodynamic circulation in the Aegean Sea referring to the development of regional upwelling coastal zones are studied by means of a mathematical model. The modeling effort is focused on the tracing of coastal areas, where upwelling events are frequently observed during the summer meteorological conditions. These areas are characterized by the enrichment of surface waters with nutrients and, consequently, increased fish production. The phenomenon is studied by the use of a two-layer mathematical model comprising the surface heated zone and the rest of the water column. The numerical solution of the model is based on the finite differences method. The wind shear applied over the stratified basin, with predefined density stratification and initial water-layers thickness, and the gravity and Coriolis forces taken into account, constitute the basic external factors for the generation of the hydrodynamic circulation in the area of the Aegean Sea. The calibration and the validation of the model are performed by the comparison of the model output to the data and observations reported in valid scientific sources. The aim of the paper is to demonstrate the significant contribution of numerical models to the better understanding of the hydrodynamics governing the Aegean water circulation as well as the tracing of upwelling zones.
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Harper, S. R., and M. T. Suidan. "Anaerobic Treatment Kinetics: Discussers' Report." Water Science and Technology 24, no. 8 (October 1, 1991): 61–78. http://dx.doi.org/10.2166/wst.1991.0218.
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A discussion of principles guiding the experimental elucidation of microbial growth and substrate utilization kinetics, and the development of mathematical models for anaerobic wastewater treatment systems, is presented. Recent developments in the areas of anaerobic treatment microbiology (including biomass characterization), biochemical mechanisms, microbial growth dyamics, reactor hydrodynamics, and mathematical modeling approaches are presented and explored.
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Bogdevicius, Marijonas, Jolanta Janutėnienė, and Oleg Vladimirov. "Simulation of Hydrodynamics Processes of Hydraulic Braking System of Vehicle." Solid State Phenomena 147-149 (January 2009): 296–301. http://dx.doi.org/10.4028/www.scientific.net/ssp.147-149.296.
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The 3D vehicle with the hydraulic braking system and disc brake with the wheel has been investigated. The dynamic models of the disk brake assembly and the wheel have been constructed. The automobile hydraulic braking system consisting of two contours is considered. . The mathematical model of the hydraulic braking system is presented, where the flow of liquid and the interaction of liquid with the rigid bodies are taken into account. The flow of fluid in a hydraulic system is described by a system of equations of a hyperbolic type, which is solved by a characteristics method. During the mathematical simulations and natural experimentations the following results were achieved. The systems of equations of dynamic models’ motions are solved by numerical methods. The dynamic characteristics of the braking system of the automobile are obtained. The results of extreme braking tests and calculations are presented.
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Bondarenko, V. I., V. V. Bilousov, F. V. Nedopekin, and J. I. Shalapko. "The Mathematical Model of Hydrodynamics and Heat and Mass Transfer at Formation of Steel Ingots and Castings." Archives of Foundry Engineering 15, no. 1 (March 1, 2015): 13–16. http://dx.doi.org/10.1515/afe-2015-0003.
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Abstract The generic mathematical model and computational algorithm considering hydrodynamics, heat and mass transfer processes during casting and forming steel ingots and castings are offered. Usage domains for turbulent, convective and non-convective models are determined depending on ingot geometry and thermal overheating of the poured melt. The expert system is developed, enabling to choose a mathematical model depending on the physical statement of a problem.
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Гольдман, Н. Л. "Study of some mathematical models for nonstationary filtration processes." Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), no. 1 (January 13, 2020): 1–12. http://dx.doi.org/10.26089/nummet.v21r101.
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Рассматриваются математические модели, связанные с изучением нестационарных процессов фильтрации в подземной гидродинамике. Они представляют собой нелинейные задачи для параболических уравнений с неизвестной функцией источника в правой части. Одна из постановок является системой, которая состоит из краевой задачи с граничными условиями первого рода и из уравнения, задающего закон изменения по времени искомой функции источника. В другой постановке соответствующая система включает в себя краевую задачу с граничными условиями второго рода. Указанные постановки существенно отличаются от обычных краевых задач для параболических уравнений. Цель исследования - установить для этих нелинейных параболических задач условия однозначной разрешимости в классе гладких функций на основе априорных оценок метода Ротэ. We consider some mathematical models connected with the study of nonstationary filtration processes in underground hydrodynamics. These models involve nonlinear problems for parabolic equations with unknown source functions. One of the problems is a system consisting of a boundary value problem of the first kind and an equation describing a time dependence of the sought source function. In the other problem, the corresponding system is distinguished from the first one by boundary conditions of the second kind. These problems essentially differ from usual boundary value problems for parabolic equations. The aim of our study is to establish conditions of unique solvability in a class of smooth functions for the considered nonlinear parabolic problems. The proposed approach involves the proof of a priori estimates for the Rothe method.
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Mazurov, Mikhail. "Nonlinear Concave Spiral Waves in Active Media Transferring Energy." EPJ Web of Conferences 224 (2019): 02011. http://dx.doi.org/10.1051/epjconf/201922402011.
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Spiral concave autowaves are widely implemented in physics, chemistry, hydrodynamics, meteorology and other fields. A mathematical model of spiral concave autowaves based on the Fitzhugh-Nagumo equation and modified axiomatic models are presented. The existence of spiral concave autowaves transferring energy was predicted via computational experiments. Applications of spiral concave autowaves carrying energy in hydrodynamics, generation of tornadoes, breaking waves, and tsunamis and examples of such autowaves in biology and medicine are reviewed and the importance of concave spiral autowaves transferring energy is emphasized.
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Giorgi, Giuseppe, Josh Davidson, Giuseppe Habib, Giovanni Bracco, Giuliana Mattiazzo, and Tamás Kalmár-Nagy. "Nonlinear Dynamic and Kinematic Model of a Spar-Buoy: Parametric Resonance and Yaw Numerical Instability." Journal of Marine Science and Engineering 8, no. 7 (July 9, 2020): 504. http://dx.doi.org/10.3390/jmse8070504.
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Mathematical models are essential for the design and control of offshore systems, to simulate the fluid–structure interactions and predict the motions and the structural loads. In the development and derivation of the models, simplifying assumptions are normally required, usually implying linear kinematics and hydrodynamics. However, while the assumption of linear, small amplitude motion fits traditional offshore problems, in normal operational conditions (it is desirable to stabilize ships, boats, and offshore platforms), large motion and potential dynamic instability may arise (e.g., harsh sea conditions). Furthermore, such nonlinearities are particularly evident in wave energy converters, as large motions are expected (and desired) to enhance power extraction. The inadequacy of linear models has led to an increasing number of publications and codes implementing nonlinear hydrodynamics. However, nonlinear kinematics has received very little attention, as few models yet consider six degrees of freedom and large rotations. This paper implements a nonlinear hydrodynamic and kinematic model for an archetypal floating structure, commonplace in offshore applications: an axisymmetric spar-buoy. The influence of nonlinear dynamics and kinematics causing coupling between modes of motion are demonstrated. The nonlinear dynamics are shown to cause parametric resonance in the roll and pitch degrees of freedom, while the nonlinear kinematics are shown to potentially cause numerical instability in the yaw degree of freedom. A case study example is presented to highlight the nonlinear dynamic and kinematic effects, and the importance of including a nominal restoring term in the yaw DoF presented.
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Sukhinov, A. I., A. E. Chistyakov, S. V. Protsenko, and E. A. Protsenko. "Vertical turbulent exchange structure and parametrization for 3D shallow water hydrodynamics models." Journal of Physics: Conference Series 2131, no. 2 (December 1, 2021): 022017. http://dx.doi.org/10.1088/1742-6596/2131/2/022017.
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Abstract The work describes research of vertical turbulent exchange structure and parametrization for 3D shallow water hydrodynamics models. In this paper, the coefficients of horizontal turbulent exchange are calculated using a whole set of averaging periods of turbulent velocity pulsations. Using experimental data on the pulsations of the velocity components, the coefficient of vertical turbulent exchange was calculated on the basis of various approaches to its parameterization, based on the analysis of the obtained coefficient distributions, the most adequate parameterization of the coefficient was selected, which is used in the software package. The distribution of the vertical turbulent exchange coefficient obtained in a numerical experiment was compared with the results of full-scale measurements, and the calculation results obtained using the mathematical statistics apparatus were analysed.
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Khvostov, A. A., A. A. Zhuravlev, E. A. Shipilova, R. S. Sumina, G. O. Magomedov, and I. A. Khaustov. "Simulink models of technological systems with perfect mixing and plug-flow hydrodynamics." Proceedings of the Voronezh State University of Engineering Technologies 81, no. 3 (December 20, 2019): 28–38. http://dx.doi.org/10.20914/2310-1202-2019-3-28-38.
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The dynamic models of elements of technological systems with perfect mixing and plug-flow hydrodynamics are based on the systems of algebraic and differential equations that describe a change in the basic technological parameters. The main difficulty in using such models in MathWorks Simulink™ computer simulation systems is the representation of ordinary differential equations (ODE) and partial differential equations (PDE) that describe the dynamics of a process as a MathWorks Simulink™ block set. The study was aimed at developing an approach to the synthesis of matrix dynamic models of elements of technological systems with perfect mixing and plug-flow hydrodynamics that allows for transition from PDE to an ODE system on the basis of matrix representation of discretization of coordinate derivatives. The process of synthesis of the dynamic matrix mathematical model was considered by the example of a sugar syrup cooler, the quality indicator of the finished product are selected as sucrose crystals and their portion in the total volume of caramel mass. Taking into account the dependence of syrup viscosity on temperature, thermal effects as a result of the process of crystallization of sucrose from syrup, design features of a typical caramel machine made it possible to clarify the dynamics of the process of syrup cooling. The model developed with this approach allows to obtain real-time estimates of temperatures at the outlet of the cooler, which makes it possible to study the dynamics of the technological process and synthesize the control system. The presented approach allows to implement mathematical models of ideal reactors in Simulink system and to move to matrix ordinary differential equations, which makes it possible to convert them into Simulink blocks. The approach is also applicable to other models of ideal reactors, which allows to form libraries of typical ideal reactors of Simulink system for synthesis of heat and mass exchange equipment. The proposed approach significantly simplifies the study and modernization of the current and the development of new technological equipment, as well as the synthesis of algorithms for controlling the processes therein.
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Niu, X. D., C. Shu, Y. T. Chew, and T. G. Wang. "Investigation of Stability and Hydrodynamics of Different Lattice Boltzmann Models." Journal of Statistical Physics 117, no. 3-4 (November 2004): 665–80. http://dx.doi.org/10.1007/s10955-004-2264-x.
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Nadolin, Konstantin Arkadevich. "Simplified three-dimensional mathematical models of hydrodynamics and passive mass transfer in calm channel flows." Итоги науки и техники Серия «Современная математика и ее приложения Тематические обзоры» 196 (2021): 66–89. http://dx.doi.org/10.36535/0233-6723-2021-196-66-89.
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O'Neill, F. G., and A. Ivanović. "The physical impact of towed demersal fishing gears on soft sediments." ICES Journal of Marine Science 73, suppl_1 (August 18, 2015): i5—i14. http://dx.doi.org/10.1093/icesjms/fsv125.
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Abstract An improved understanding of the physical interaction of towed demersal fishing gears with the seabed has been developed in recent years, and there is a clearer view of the underpinning mechanical processes that lead to the modification and alteration of the benthic environment. The physical impact of these gears on soft sediments can be classified broadly as being either geotechnical or hydrodynamic in nature: penetration and piercing of the substrate, lateral displacement of sediment, and the influence of the pressure field transmitted through the sediment can be considered geotechnical, whereas the mobilization of sediment into the water column can be considered hydrodynamic. A number of experimental and numerical approaches have been used to gain better insights of these physical processes. These include small-scale modelling in towing tanks and sand channels; large-scale modelling in the field; measurements behind full-scale towed gears at sea; numerical/mathematical modelling of sediment mechanics; and numerical/mathematical modelling of hydrodynamics. Here, we will review this research, and that in associated fields, and show how it can form the basis of predictive models of the benthic impact of trawl gears.
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Panasenko, Natalia, Nikolay Motuz, and Asya Atayan. "Assimilation and processing of observation data obtained by satellite earth sensing for monitoring the current state of heterogeneous objects on the water surface." E3S Web of Conferences 224 (2020): 02030. http://dx.doi.org/10.1051/e3sconf/202022402030.
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The study is devoted to the analysis of satellite observations data assimilation to discover the necessary information for developing and verifying mathematical models of hydrodynamics and biological shallowwater kinetics. The use of satellite earth sensing data is taken to enhance information base. The possible use of neural networks with optical flow computation is considered in the study. The objective of the study is to develop a software tool used to identify the initial conditions in mathematical modeling of hydrobilogical shallow-water processes.
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Shevtsov, Nikita O., Sergei V. Stepanov, and Tatiana A. Pospelova. "THE STUDY OF THE PREDICTIVE ABILITY OF NUMERICAL AND ANALYTICAL MODELS (THE CASE OF MUTUAL WELL IMPACT EVALUATION)." Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy 6, no. 3 (2020): 131–42. http://dx.doi.org/10.21684/2411-7978-2020-6-3-131-142.
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The main purpose of any model is to provide an opportunity to study the model object and the processes running in it for obtaining the predictive characteristics, among other reasons. In this connection, it is important to know, which mathematical models can help in analyzing and supporting oil deposit development, in particular, in assessing the mutual influence of production and injection wells. The characteristic features of mathematical modeling of field development include the oil deposits being located in natural formations that cannot be directly observed, as well as the complex filtration processes taking place in the formations due to the formation structure. Therefore, the mathematical modeling of development can be both complex and simple. On the one hand, it may use complex numerical hydrodynamic models, based on the understanding of spatial distribution of reservoir properties, which have an opportunity for detailed description of filtration processes. On the other hand, the modeling may use relatively simple analytical models, which have no need to specify the spatial distribution of properties; yet, the description of filtration processes is significantly simplified in comparison with hydrodynamics. Therefore, the practical value of the modeling result depends on the right approach to modeling. The task of estimating the mutual influence of wells requires the choice of numerical or analytical model to be based on understanding of the predictive ability of the models under consideration. Since such ability depends both on the ability to describe filtration processes in detail and on the need to take into account the spatial distribution of reservoir properties, it is initially impossible to conclude, which model has the best predictive ability. It becomes possible to reveal the level of predictive ability when considering the problem of mutual well impact assessment for synthetic models of oil deposits. This article presents the results of studies in the case of ten synthetic models. Numerical hydrodynamic models and analytical CRM models were set up for “actual” data of well operation. Using the retrospective test method, the authors have shown that the analytical models have a higher predictive power than the numerical models.
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Bobkov, S. P., and A. S. Chernjavskaja. "Simulation of continuous flows with discrete models." Vestnik IGEU, no. 3 (2019): 68–75. http://dx.doi.org/10.17588/2072-2672.2019.3.068-075.
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The vast majority of heat and power processes include the motion of significant amounts of gases and liq-uids. This makes it important and quite urgent to develop approaches for computer simulation and visualiza-tion of continuum flows in technological devices and pipelines. A whole set of new approaches to mathematical modelling of continuum flows has been recently developed. The most common one is using discrete mathematical models for these purposes. Discrete approaches can simplify modeling procedures in cases where traditional methods require complex time-consuming calculations. At the same time, correct-ness of description of various flow regimes by the discrete methods is often questioned. The second problem of the mentioned models is a large-scale transition from model discrete parameters to generally accepted macroscopic characteristics of flows. The purpose of this work is to determine continuous flow regimes that can be correctly described by certain models. The paper considers discrete dynamic models in the form of lattice gases. A continuum in this case is represented by a set of particles moving only in allowed directions. Despite certain limitations, there is solid evidence that lattice gases quite successfully describe a whole range of hydrodynamic phenomena, and the obtained results do not contradict the generally accepted views on the physical nature of continuum motion processes. The paper describes approaches that allow estimating flow parameters using generally accepted macroscopic indicators. It also studies possible application areas of lattice gas models using the motion of virtual particles on a spatial lattice (HPP and FHP models) and the model based on the discrete analogue of the Boltzmann equation (LBM model) to simulate and visualize continuum flows. The obtained data are in good agreement with the generally accepted results and do not contradict the provisions of classical hydrodynamics. The paper shows that the models considering particle collisions (HPP and FHP) are applicable to describing gas flows in laminar regimes. The LBM model should be considered to be more correct for simulation and visualization of real fluid flows.
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Morgenroth, E., H. Eberl, and M. C. van Loosdrecht. "Evaluating 3-D and 1-D mathematical models for mass transport in heterogeneous biofilms." Water Science and Technology 41, no. 4-5 (February 1, 2000): 347–56. http://dx.doi.org/10.2166/wst.2000.0465.
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Results from a three dimensional model for heterogeneous biofilms including the numerical solution of hydrodynamics were compared to simplified one dimensional models. A one dimensional model with a variable diffusion coefficient over the thickness of the biofilm was well suited to approximate average concentration profiles of three dimensional simulations of rough biofilms. A new compartmentalized one dimensional model is presented that is then used to evaluate effects of pores and channels on microbial competition in heterogeneous biofilms. Surface and pore regions of the biofilm are modeled using separate compartments coupled by a convective link. Local concentration profiles from the three dimensional simulations could be adequately reproduced using the compartmentalized one dimensional model. The compartmentalized one dimensional model was then used to evaluate bacterial competition in a growing biofilm and in a mushroom type biofilm assuming different modes of detachment.
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Ferreira, Rui M. L., Mário J. Franca, João G. A. B. Leal, and António H. Cardoso. "Mathematical modelling of shallow flows: Closure models drawn from grain-scale mechanics of sediment transport and flow hydrodynamicsThis paper is one of a selection of papers in this Special Issue in honour of Professor M. Selim Yalin (1925–2007)." Canadian Journal of Civil Engineering 36, no. 10 (October 2009): 1605–21. http://dx.doi.org/10.1139/l09-033.
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Mathematical modelling of river processes is, nowadays, a key element in river engineering and planning. River modelling tools should rest on conceptual models drawn from mechanics of sediment transport, river mechanics, and river hydrodynamics. The objectives of the present work are (i) to describe conceptual models of sediment transport, deduced from grain-scale mechanics of sediment transport and turbulent flow hydrodynamics, and (ii) to present solutions to specific river morphology problems. The conceptual models described are applicable to the morphologic evolution of rivers subjected to the transport of poorly sorted sediment mixtures at low shear stresses and to geomorphic flows featuring intense sediment transport at high shear stresses. In common, these applications share the fact that sediment transport and flow resistance depend, essentially, on grain-scale phenomena. The idealized flow structures are presented and discussed. Numerical solutions for equilibrium and nonequilibrium sediment transport are presented and compared with laboratory and field data.
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Masselot, A., and B. Chopard. "A Multiparticle Lattice-Gas Model for Hydrodynamics." International Journal of Modern Physics C 09, no. 08 (December 1998): 1221–30. http://dx.doi.org/10.1142/s0129183198001102.
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Cellular automata (CA) and lattice-Boltzmann (LB) models are two possible approaches to simulate fluid-like systems. CA models keep track of the many-body correlations and provide a description of the fluctuations. However, they lead to a noisy dynamics and impose strong restrictions on the possible viscosity values. On the other hand, LB models are numerically more efficient and offer much more flexibility to adjust the fluid parameters, but they neglect fluctuations. Here we discuss a multiparticle lattice model which reconciles both approaches. Our method is tested on Poiseuille flows and on the problem of ballistic annihilation in two dimensions for which the fluctuations are known to play an important role.
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BILIAIEV, M. M., V. A. KOZACHYNA, P. B. MASHYKHINA, and V. V. TSURKAN. "MATHEMATICAL MODELING IN WATER TREATMENT PROBLEMS." Ukrainian Journal of Civil Engineering and Architecture, no. 4 (October 22, 2022): 13–19. http://dx.doi.org/10.30838/j.bpsacea.2312.250822.13.872.
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Problem statement. Analysis of the treatment facilities efficiency in sewerage at the stage of their design is great importance. Also, at the stage of structures’ reconstruction or their operation adjustment under different load conditions, it is necessary to know the efficiency of water treatment in different areas of treatment facilities. Such information makes it possible to rationally operate facilities. For solving problems of this class, the most effective tool is the use of the numerical modeling method. The work considers development of numerical models set for solving problems of this class. Methodology. Two fundamental models are used to solve the velocity field determination of the wastewater flow in the sewage treatment plant. The first is a model of the vortex-free motion for an incompressible fluid. The second model is the Navier-Stokes equations written in Helmholtz variables. The mass transfer equation is used to determine impurity concentration fields in sewage treatment plants, which takes into account flow velocity, diffusion and the presence of impurity emission sources. Material balance equations for the substrate and activated sludge are used to calculate the process of biological wastewater treatment. Finite-difference schemes are used to build numerical models that allow calculating the hydrodynamics of the flow and the distribution of the impurity concentration in the facility. The Euler method is used for the numerical solution of the material balance equations. Results. Numerical models were built, which were used to develop a complex of computer programs. These computer programs allow real-time analysis of the water treatment efficiency in the facility. Scientific novelty. Numerical models have been developed that allow investigating the process of water treatment in facilities of the «settler» type and in aeration tanks, that is, for a significant class of treatment facilities used in practice. Practical value. The calculation time of the velocity field and the impurity concentration field in a water treatment plant with a complex geometric shape is few seconds. This allows usinge the developed numerical models for serial calculations in project organizations in daily work.
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Суровежко, А. С., and С. И. Мартыненко. "On optimization of technical devices based on a hierarchy of mathematical models." Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), no. 4 (September 10, 2019): 411–27. http://dx.doi.org/10.26089/nummet.v20r436.
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Рассмотрена задача о топливном коллекторе, которую можно отнести к обратным задачам гидродинамики: необходимо определить геометрию распределительного канала коллектора, обеспечивающего равномерную раздачу топлива. Однако профилирование коллектора на основе 3D стационарных уравнений Навье-Стокса для турбулентного течения несжимаемой вязкой среды в шероховатых каналах требует непрактичных вычислительных усилий. Использована иерархия математических моделей: 1D уравнения Навье-Стокса для профилирования и 3D уравнения Навье-Стокса для калибровки 1D модели. Показано, что используемая иерархия моделей позволяет существенно снизить объем вычислительной работы, необходимой для расчета оптимальной конструкции коллектора. Предложенный подход представляет интерес для оптимизации технических устройств различного назначения. A fuel collector problem is considered as an inverse problem of hydrodynamics: it is necessary to determine the distribution channel geometry of a collector for a uniform fuel distribution. However, the collector profiling based on the 3D stationary Navier-Stokes equations for turbulent flow of an incompressible viscous medium in rough channels requires impractical computational efforts. A hierarchy of mathematical models (1D Navier-Stokes equations for the collector profiling and 3D Navier-Stokes equations for 1D model validation) is used in this paper. It is shown that the hierarchy of models can significantly reduce amount of computational work needed for computing the optimal collector design. The developed approach is of interest for optimizing technical devices for various purposes.
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Nikitina, Alla, Alena Filina, and Alexander Chistyakov. "Mathematical modeling of hydrodynamic processes in shallow waters in the presence of pollutants of various origin, as well as areas covered with plastic waste." E3S Web of Conferences 363 (2022): 02024. http://dx.doi.org/10.1051/e3sconf/202236302024.
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The paper covers the modeling of hydrodynamic processes in shallow waters in the presence of pollutants of various types, as well as areas covered with plastic waste, including nano- and microplastics. The simulation performed using new and effective mathematical instruments, including assimilation methods of measurement data, restoration of the state function, diagnostics of quality of the developed models, the research the sensitivity of models to variations in input data, the integration of models with various scales. Interrelated non-stationary, spatially inhomogeneous mathematical models of hydrodynamics and biological kinetics of shallow waters were developed and numerically implemented. They describe non-linear processes of hydrophysics, biogeochemical cycles, transport and transformation of suspensions and sediments with microplastic particles and other pollutants, absorption of it by zooplankton and fish, movement of plastic particles through food, the forecast of their impact on the main hydrobionts of shallow waters of the Azov-Black Sea basin, including the Azov Sea, Taganrog Bay, Gelendzhik Bay. The models take into account the heat and salt transport; the complex, dynamically changing water geometry; friction on the bottom and wind stresses; turbulent and advective heat and mass exchange in three coordinate directions; the Coriolis force; river flows; evaporation, temperature and oxygen regimes. They make it possible to improve the accuracy of hydrophysical processes modeling in shallow waters, to detect vortex structures of currents that can be a natural pollution traps, including microplastic. Based on a supercomputer, a complex of application has been designed and adapted for solving predictive problems of water ecology and water resources management.
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Van Wassenbergh, Sam, and Peter Aerts. "Aquatic suction feeding dynamics: insights from computational modelling." Journal of The Royal Society Interface 6, no. 31 (September 9, 2008): 149–58. http://dx.doi.org/10.1098/rsif.2008.0311.
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Aquatic suction feeding in vertebrates involves extremely unsteady flow, externally as well as internally of the expanding mouth cavity. Consequently, studying the hydrodynamics involved in this process is a challenging research area, where experimental studies and mathematical models gradually aid our understanding of how suction feeding works mechanically. Especially for flow patterns inside the mouth cavity, our current knowledge is almost entirely based on modelling studies. In the present paper, we critically discuss some of the assumptions and limitations of previous analytical models of suction feeding using computational fluid dynamics.
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Holm, Darryl D., Jonathan I. Rawlinson, and Cesare Tronci. "The bohmion method in nonadiabatic quantum hydrodynamics." Journal of Physics A: Mathematical and Theoretical 54, no. 49 (November 19, 2021): 495201. http://dx.doi.org/10.1088/1751-8121/ac2ae8.
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Abstract Starting with the exact factorization of the molecular wavefunction, this paper presents the results from the numerical implementation in nonadiabatic molecular dynamics of the recently proposed bohmion method. Within the context of quantum hydrodynamics, we introduce a regularized nuclear Bohm potential admitting solutions comprising a train of δ-functions which provide a finite-dimensional sampling of the hydrodynamic flow paths. The bohmion method inherits all the basic conservation laws from its underlying variational structure and captures electronic decoherence. After reviewing the general theory, the method is applied to the well-known Tully models, which are used here as benchmark problems. In the present case of study, we show that the new method accurately reproduces both electronic decoherence and nuclear population dynamics.
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Eyink, Gregory, Joel L. Lebowitz, and Herbert Spohn. "Hydrodynamics of stationary non-equilibrium states for some stochastic lattice gas models." Communications in Mathematical Physics 132, no. 1 (August 1990): 253–83. http://dx.doi.org/10.1007/bf02278011.
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A. I., Sukhinov, Protsenko S.V., and Panasenko N. D. "MATHEMATICAL MODELING AND ECOLOGICAL DESIGN OF THE MARINE SYSTEMS TAKING INTO ACCOUNT MULTI-SCALE TURBULENCE USING REMOTE SENSING DATA." Computational Mathematics and Information Technologies 1, no. 3 (December 31, 2022): 104–13. http://dx.doi.org/10.23947/2587-8999-2022-1-3-104-113.
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The paper considers a mathematical model of biological kinetics and geochemical cycles based on a system of convection-diffusion equations with nonlinear coefficients, supplemented by a spatially inhomogeneous three-dimensional mathematical model of wave hydrodynamics of a shallow reservoir, with a refined coefficient of turbulent vertical exchange. The task of monitoring the water surface in order to detect phytoplankton spots involves the creation and verification of effective methods for clustering these objects on the surface of reservoirs, in particular, restoring their boundaries based on remote sensing data. The article uses multispectral satellite images as sounding data. Based on the obtained images of plankton populations, the initial conditions for mathematical models of biogeochemical cycles can be determined, on the basis of which prognostic calculations are performed.
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Sukhinov, Alexander, Alexander Chistyakov, Inna Kuznetsova, Yulia Belova, and Alla Nikitina. "Mathematical Model of Suspended Particles Transport in the Estuary Area, Taking into Account the Aquatic Environment Movement." Mathematics 10, no. 16 (August 11, 2022): 2866. http://dx.doi.org/10.3390/math10162866.
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A large amount of contaminants enter marine systems with river runoff, so the purpose of the study is to model the transport of suspended particles in the estuary area. To describe hydrodynamic and hydrophysical processes, the mathematical model of the suspended particles transport was used, supplemented by a three-dimensional mathematical model of hydrodynamics, used to calculate the fields of the aquatic environment movement velocity vector, and equation for calculating the variable density. The approximation of the equations for calculating the velocity field by spatial variables is based on the splitting schemes for physical processes with fluid volume of the control areas, which allows for us to consider the complex geometry of the coastline and the bottom. The suspended particles transport model is approximated using splitting schemes for two-dimensional and one-dimensional problems. Numerical experiments were carried out to simulate the aquatic environment movement in the estuary area, the multicomponent suspension deposition, as well as mixing of waters in the mouth, taking into account the different density of the aquatic environment. The used models and methods allow to significantly improve the accuracy of modeling suspended particle transport and consider the factors influencing the studied processes.
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Prostomolotov, Anatoly I., Nataliya A. Verezub, Natalia A. Vasilyeva, and Alexey E. Voloshin. "Hydrodynamics and Mass Transfer during the Solution Growth of the K2(Co,Ni)(SO4)2•6H2O Mixed Crystals in the Shapers." Crystals 10, no. 11 (October 29, 2020): 982. http://dx.doi.org/10.3390/cryst10110982.
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Mathematical models of the hydrodynamics and mass transfer processes during the mixed crystal growth from low-temperature aqueous solutions have been analyzed. The features of these processes are caused by complex design of the crystallizer with a shaper. Two models of the solution flowing into the shaper have been considered. In the first model, the solution is fed to the central part of the crystal. The second model presents a peripheral solution supply along the shaper perimeter, which allows us to create a swirling flow. The calculation models correspond to laminar and turbulent regimes of solution flow during the growth of K2(Co,Ni)(SO4)2•6H2O mixed crystal from an aqueous solution.
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Krutov, Anatoly, Azam Azimov, Sodiq Ruziev, and Akmal Dumanov. "Modelling of turbidity distribution along channels." E3S Web of Conferences 97 (2019): 05046. http://dx.doi.org/10.1051/e3sconf/20199705046.
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The purpose of the article is to develop the required and sufficient conditions under which numerical methods can be used for engineering calculations and for scientific research of hydrodynamic processes in solving practical problems related to surveying of pollutants diffusion in water flows. The conducted studies consisted in the finding out conditions under which mathematical modelling using hydrodynamic equations allows to solve engineering problems of channel hydrodynamics and, in particular, to numerically simulate the transport of suspended particles in channels. A number of additional nature of numerical models were studied in addition to approximation and stability, such as averaging over probability and over time averaging. It was noted that only stationary processes could be described by equations if they are obtained from the Reynolds equations, i.e. when using the Reynolds equations, an important class of problems with a pulsating flow under constant boundary conditions is excluded from consideration. And, if the equations are obtained directly from the conservation laws, then all the desired variables have the meaning of actual quantities averaged over the scale. That is even in the case of statistically stationary flows, using such equations, it is possible to solve nonstationary problems on large time scales.
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Kugler, Susanne Katrin, Armin Kech, Camilo Cruz, and Tim Osswald. "Fiber Orientation Predictions—A Review of Existing Models." Journal of Composites Science 4, no. 2 (June 8, 2020): 69. http://dx.doi.org/10.3390/jcs4020069.
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Fiber reinforced polymers are key materials across different industries. The manufacturing processes of those materials have typically strong impact on their final microstructure, which at the same time controls the mechanical performance of the part. A reliable virtual engineering design of fiber-reinforced polymers requires therefore considering the simulation of the process-induced microstructure. One relevant microstructure descriptor in fiber-reinforced polymers is the fiber orientation. This work focuses on the modeling of the fiber orientation phenomenon and presents a historical review of the different modelling approaches. In this context, the article describes different macroscopic fiber orientation models such as the Folgar-Tucker, nematic, reduced strain closure (RSC), retarding principal rate (RPR), anisotropic rotary diffusion (ARD), principal anisotropic rotary diffusion (pARD), and Moldflow rotary diffusion (MRD) model. We discuss briefly about closure approximations, which are a common mathematical element of those macroscopic fiber orientation models. In the last section, we introduce some micro-scale numerical methods for simulating the fiber orientation phenomenon, such as the discrete element method (DEM), the smoothed particle hydrodynamics (SPH) method and the moving particle semi-implicit (MPS) method.
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Horel, Boris. "Review of Existing Benchmarks and Databases for Sailing Vessels." Journal of Sailing Technology 7, no. 01 (February 2, 2022): 52–87. http://dx.doi.org/10.5957/jst/2022.7.3.52.
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Benchmarks are of great interest when trying to validate innovative tools or new mathematical models. They also allow academics and industrials to better estimate the accuracy of their tools compared to the current state of the art. This paper tends to present a review of existing benchmarks and databases in naval hydrodynamics, including aerodynamic phenomena on ships with the aim of evaluating the applicability of such benchmarks to sailing vessels. This paper also tends to estimate the relevance of proposing new benchmarks and their contributions to the yacht research community.
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Panasenko, Natalia, Marina Ganzhur, Alexey Ganzhur, and Vladimir Fathi. "Multichannel satellite image application for water surface objects identification." E3S Web of Conferences 210 (2020): 07005. http://dx.doi.org/10.1051/e3sconf/202021007005.
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The paper is devoted to the analysis of methods of adoption of satellite observation data in order to identify the required information used in the development and verification of mathematical models of hydrodynamics and biological kinetics of shallow water reservoirs. For the information accumulation, we consider the use of remote sensing data. The aim of the paper is to identify the best implementation method for software tools in order to improve the quality of assimilation of date of satellite sensing of the Earth relating to hydrobiological processes in a shallow water reservoir.
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Sutulo, S., and C. Guedes Soares. "Development of a Multifactor Regression Model of Ship Maneuvering Forces Based on Optimized Captive-Model Tests." Journal of Ship Research 50, no. 04 (December 1, 2006): 311–33. http://dx.doi.org/10.5957/jsr.2006.50.4.311.
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The paper provides the results of model tests planned with an optimized experimental design method. Captive-model tests have been carried out according to such a design on a computerized planar-motion carriage with a model of a fast catamaran with five varying factors (drift angle, rate-of-yaw amplitude, sinkage, trim and heel angles) and with all six force/moment components measured at each run. The measured values were used after preprocessing for construction of polynomial regression models for all force components acting upon the catamaran's hulls. It is demonstrated that the optimized experimental design method allows rather complicated mathematical models for maneuvering hydrodynamics forces to be obtained from captive model tests at a reasonable level of effort.
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Nesterov, S. A., and I. S. Egorov. "Analysis of processes in magnetorheological sealer considering for magnetic fluid deformation." Vestnik IGEU, no. 1 (February 28, 2022): 54–63. http://dx.doi.org/10.17588/2072-2672.2022.1.054-063.
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The small size of the working gap in the sealer makes many physical measurements difficult or impossible. The main way to study the processes inside the device is to use analytical and numerical mathematical modeling. Most researchers apply finite-element calculation of magnetic field and analytically find the difference in pressure. Currently, there are few studies devoted to multiphysics numerical calculations of the processes in magnetorheological seal. The use of numerical models allows considering the dependence of rheological properties of magnetic fluid on hydrodynamic, temperature and magnetic fields, the real geometry of the working zone. Compared to the analytical models, a numerical one includes a smaller number of assumptions and allows visualizing various flow parameters, which are especially important for the analysis. The purpose of this study is to analyze the effect of the deformation of the magnetorheological plug in case of pressure difference held by the sealer. The study is based on the developed numerical model with the related calculation of magnetic and hydrodynamic fields. The study is carried out based on the theories of ferrohydrodynamics, hydrodynamics and electromagnetic field. Integrated finite-element modeling of the magnetic and hydrodynamic fields of the magnetorheological sealer in Comsol Мultiphysics has been used. A numerical model of the magnetorheological sealer characterized by automatic rearrangement of the boundaries of the liquid plug based on the balance of pressures inside the liquid has been developed. The distribution results of magnetic induction and pressure in the working gap of the sealer, considering changes in the boundaries of the magnetic fluid, has been obtained. Comparison of the results of the obtained retained pressure drop and the results of other models has been carried out. A numerical mathematical model that considers the deformation of the magnetorheological plug has been developed. The model makes it possible to estimate the influence of centrifugal forces of the rotating shaft on the retained pressure drop. The results can be used to create high-speed seal components. The difference of the value of analytical calculation does not exceed 5 %. The assumption about full filling of the working gap with magnetic fluid 2,5 times underestimates the retained pressure difference at high shaft rotation speeds.
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Qiu, Shu Xia, and Ning Pang. "A Numerical Study on the Flow Characteristics of Opposed Impinging Jets." Advanced Materials Research 516-517 (May 2012): 854–57. http://dx.doi.org/10.4028/www.scientific.net/amr.516-517.854.
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Inspired by the increasing interests on mixing effectiveness of opposed impinging jets, a numerical work is carried out to study the flow characteristics. The fluid temperature is used as a passive tracer to evaluate the mixing rate in the current mathematical models. The effect of Reynolds number on the mixing performance is discussed. Furthermore, in order to enhance the mixing efficiency and reduce the energy cost, unsteady flow pulsations are induced at the jet inlets. The numerical results indicate that the mixing efficiency can be improved by the unsteady flow pulsations via adjusting the hydrodynamics characteristics in the opposed jets.
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Basha, Omar M., Laurent Sehabiague, Ahmed Abdel-Wahab, and Badie I. Morsi. "Fischer–Tropsch Synthesis in Slurry Bubble Column Reactors: Experimental Investigations and Modeling – A Review." International Journal of Chemical Reactor Engineering 13, no. 3 (September 1, 2015): 201–88. http://dx.doi.org/10.1515/ijcre-2014-0146.
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Abstract This paper presents an extensive review of the kinetics, hydrodynamics, mass transfer, heat transfer and mathematical as well as computational fluid dynamics (CFD) modeling of Low-Temperature Tropsch Synthesis (LTFT) synthesis in Slurry Bubble Column Reactors (SBCRs), with the aim of identifying potential research and development areas in this particular field. The kinetic expressions developed for F-T synthesis over iron and cobalt catalysts along with the water gas shift (WGS) reactions are summarized and compared. The experimental data and empirical correlations to predict the hydrodynamics (gas holdup, Sauter mean bubble diameter, and bubble rise velocity), mass transfer coefficients and heat transfer coefficients are presented. The effects of various operating variables, including pressure, temperature, gas velocity, catalyst concentration, reactor geometry, and reactor internals on the hydrodynamic and transport parameters as well as the performance of SBCRs are discussed. Additionally, modeling efforts of SBCRs, using axial dispersion models (ADM), multiple cell recirculation models (MCCM) and computational fluid dynamics (CFD), are addressed. This review revealed the following: (1)Numerous F-T and WGS kinetic rate expressions are available for cobalt and iron catalysts and one must be careful in selecting the appropriate expressions for LTFT. Iron catalyst suffers from severe attrition and subsequent deactivation in SBCRs and accordingly building a costly catalyst manufacturing facility onsite is required to maintain a steady operation of the F-T reactor; (2)Experimental data on the hydrodynamic and transport parameters at high pressures and temperatures, typical to those of actual F-T synthesis, remain scanty when compared with the plethora of studies conducted using air–water systems in small reactors at ambient conditions; (3)Several empirical correlations for predicting the hydrodynamic and mass as well heat transfer parameters are available and one should select those which consider the reactor diameter, gas mixtures and the potential foamability of the F-T liquids; (4)The effect of cooling internals configuration and sparger design on the hydrodynamic and transport parameters, local turbulence, mixing and catalyst attrition are yet to be seriously addressed; (5)The impact of operating variables on the hydrodynamic and transport parameters as well as the overall performance of the SBCRs should be investigated using actual F-T fluid–solid systems under typical pressures and temperatures using a large-scale reactor (>0.15 m ID) in the presence of gas spargers and cooling internals; (6)Significant efforts are still required in order to advance CFD modeling of SBCRs, particularly those pertaining to the relevant closure models, such as drag, lift and turbulence. Also, cooling internals configuration and the design as well as orientation of gas spargers should be accounted for in the CFD modeling; and (7)Proper validations of the CFD formulations using actual systems for F-T SBCR are needed.
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Canivete Cuissa, José R., and Oskar Steiner. "Vortices evolution in the solar atmosphere." Astronomy & Astrophysics 639 (July 2020): A118. http://dx.doi.org/10.1051/0004-6361/202038060.
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Aims. We study vortex dynamics in the solar atmosphere by employing and deriving the analytical evolution equations of two vortex identification criteria. Methods. The two criteria used are vorticity and the swirling strength. Vorticity can be biased in the presence of shear flows, but its dynamical equation is well known; the swirling strength is a more precise criterion for the identification of vortical flows, but its evolution equation is not known yet. Therefore, we explore the possibility of deriving a dynamical equation for the swirling strength. We then apply the two equations to analyze radiative magneto-hydrodynamical simulations of the solar atmosphere produced with the CO5BOLD code. Results. We present a detailed review of the swirling strength criterion and the mathematical derivation of its evolution equation. This equation did not exist in the literature before and it constitutes a novel tool that is suitable for the analysis of a wide range of problems in (magneto-)hydrodynamics. By applying this equation to numerical models, we find that hydrodynamical and magnetic baroclinicities are the driving physical processes responsible for vortex generation in the convection zone and the photosphere. Higher up in the chromosphere, the magnetic terms alone dominate. Moreover, we find that the swirling strength is produced at small scales in a chaotic fashion, especially inside magnetic flux concentrations. Conclusions. The swirling strength represents an appropriate criterion for the identification of vortices in turbulent flows, such as those in the solar atmosphere. Moreover, its evolution equation, which is derived in this paper, is pivotal for obtaining precise information about the dynamics of these vortices and the physical mechanisms responsible for their production and evolution. Since this equation is available, the swirling strength is now the ideal quantity to study the dynamics of vortices in (magneto-)hydrodynamics.
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VASILIEV, A. A. "INFLUENCE OF NUMBER OF THE HYDROSTATIC BEARINGS WITH AN INCOMPLETE RANGE ANGLE POCKETS ON STATIC AND DYNAMIC CHARACTERISTICS." Fundamental and Applied Problems of Engineering and Technology, no. 5 (2021): 52–57. http://dx.doi.org/10.33979/2073-7408-2021-349-5-52-57.
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Comparative analysis of the design of the working surface of the hydrostatic bearings with an incomplete range angle for the static and dynamic characteristics of the bearings. Rectangular pockets with two variants of the number of pockets: two, three and four were considered as constructive designs. The following were considered as static characteristics: load capacity, power losses for pumping and flow rate of the working fluid. As dynamic characteristics were considered: stiffness and damping coefficients. For the models, mathematical calculation models were used based on the joint solution of the basic equations of hydrodynamics: the Reynolds equation, the heat balance equation, the flow rate equation and a dynamic model developed for the "flexible rotor – hydrostatic bearings with an incomplete range angle" scheme, including the calculation of dynamic coefficients and the definition stable support work.
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Wang, Rui Li, Xiao Liang, Wen Zhou Lin, Xue Zhe Liu, and Yun Long Yu. "Verification and Validation of a Detonation Computational Fluid Dynamics Model." Defect and Diffusion Forum 366 (April 2016): 40–46. http://dx.doi.org/10.4028/www.scientific.net/ddf.366.40.
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Verification and validation (V&V) are the primary means to assess the accuracy and reliability in computational fluid dynamics (CFD) simulation. V&V of the multi-medium detonation CFD model is conducted by using our independently-developed software --- Lagrangian adaptive hydrodynamics code in the 2D space (LAD2D) as well as a large number of benchmark testing models. Specifically, the verification of computational model is based on the basic theory of the computational scheme and mathematical physics equations, and validation of the physical model is accomplished by comparing the numerical solution with the experimental data. Finally, some suggestions are given about V&V of the detonation CFD model.
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Shpigunova, O. I., and A. A. Glazunov. "Numerical Simulation of Pulsed Arc Welding by Melting Electrode." Materials Science Forum 575-578 (April 2008): 786–91. http://dx.doi.org/10.4028/www.scientific.net/msf.575-578.786.
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In this paper the processes of melting and transfer of an electrode metal to the molten pool, hydrodynamics of molten pool in controlled pulsed arc welding in carbon dioxide have been investigated. The process of pulsed arc welding with systematic short-circuits of the arc gap is realized by adaptive algorithms of pulsed control over main energetic parameters of welding - arc current and voltage, arc heated efficiency, peak short-circuiting current, which provide the dosage of energy for melting and transfer of every drop of an electrode metal, the control over fluidity of the weld pool. Physical and mathematical models describing such processes in CO2, original software have been developed. The results of physical simulation and mathematical modelling permit to determine the influence of energetic parameters of the process on the condition of the “power source – electrode – arc – molten pool” electrodynamic system at each moment of time.