Journal articles on the topic 'Hydrodynamics – Mathematical models; Tides – Mathematical models'
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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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Ivanchuk, Yaroslav, Oleksandr Manzhilevskyy, Ruslan Belzetskyi, Oleksandr Zamkovyi, and Roman Pavlovych. "Modelling of Piling Technology by Vibroimpact Device with Hydropulse Drive." Scientific Horizons 25, no. 1 (May 25, 2022): 9–20. http://dx.doi.org/10.48077/scihor.25(1).2022.9-20.
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Based on the analysis of the developed mathematical model, this paper proposes optimal operating modes of the vibroimpact device to ensure the intensification of driving construction piles. It is an original design of a modern, highly efficient device for driving construction piles, equipped with a compact, powerful hydraulic impulse drive unit. To develop a mathematical model of the construction pile driving technology, the following methods were used: mechanoreological phenomenology, hydrodynamics, and generalised laws of mechanics. Mathematical models of the dynamics of technological processes of driving construction piles with a vibroimpact device are improved based on a hydraulic impulse drive unit in the form of a spatial non-stationary formulation of the problem and integral equations of dynamic characteristics of the moving elements of the drive unit. The study obtained the distribution of the pressure and velocity of the working fluid in the hydraulic unit of the vibroimpact device, as well as changes in the kinematic parameters of the elements of the technological equipment based on the mathematical model developed by the finite volume method, using numerical modelling and high-performance computer systems. Optimal modes of operation of a hydraulic impulse drive of a vibroimpact device are proposed to provide an intensification of the construction pile driving technology. It was found that when low-frequency vibration is applied, the driving of construction piles is intensified. Application of a hydraulic impulse drive that is based on two-stage vibration excitation allowed implementing the vibroimpact modes of the device. The average pile driving speed with a vibroimpact interaction is five times higher compared to conventional driving methods
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Ebrahimian, H., and A. Liaghat. "Field evaluation of various mathematical models for furrow and border irrigation systems." Soil and Water Research 6, No. 2 (May 30, 2011): 91–101. http://dx.doi.org/10.17221/34/2010-swr.
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In this study, three mathematical models in the SIRMOD package including the hydrodynamic (HD), zero inertia (ZI), and kinematic wave (KW) models were tested using the data from several field experiments for both border and furrow irrigation systems. Five data sets for borders and seven data sets for furrows were used in this assessment. The results indicated that the performance of all models was satisfactory for the prediction of the advance and recession times. There was no difference in the prediction of the advance and recession times and infiltrated and runoff volumes between the hydrodynamic and zero-inertia approaches of the SIRMOD software. The HD, ZI, and KW models predicted the recession times better than the advance times for both the experimental borders and furrows. The predicted advance and recession times were estimated by these models more accurately than the infiltrated and runoff volumes. Also the accuracy of these models for the prediction of the advance and recession times was better for the experimental furrows in comparison with the experimental borders.
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Torres-Bejarano, F., C. Couder-Castañeda, H. Ramírez-León, J. J. Hernández-Gómez, C. Rodríguez-Cuevas, I. E. Herrera-Díaz, and H. Barrios-Piña. "Numerical Modelling of Heavy Metal Dynamics in a River-Lagoon System." Mathematical Problems in Engineering 2019 (May 6, 2019): 1–24. http://dx.doi.org/10.1155/2019/8485031.
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This paper describes the development of a two-dimensional water quality model that solves hydrodynamic equations tied to transport equations with reactions mechanisms inherent in the processes. This enables us to perform an accurate assessment of the pollution in a coastal ecosystem. The model was developed with data drawn from the ecosystem found in Mexico’s southeast state of Tabasco. The coastal ecosystem consists of the interaction of El Yucateco lagoon with Chicozapote and Tonalá rivers that connect the lagoon with the Gulf of Mexico. The results of pollutants transport simulation in the coastal ecosystem are presented, focusing on toxic parameters for two hydrodynamic scenarios: wet and dry seasons. As it is of interest in the zone, the transport of four metals is studied: Cadmium, Chromium, Nickel, and Lead. In order to address these objectives, a self-posed mathematical problem is solved numerically, which is based on the measured data. The performed simulations show how to characterise metals transport with an acceptable accuracy, agreeing well with measured data in total concentrations in four control points along the water body. Although for the accurate implementation of the hydrodynamic-based water quality model herein presented boundary (geometry, tides, wind, etc.) and initial (concentrations measurements) conditions are required, it poses an excellent option when the distribution of solutes with high accuracy is required, easing environmental, economic, and social management of coastal ecosystems. It ought to be remarked that this constitutes a robust differential equation-based water quality model for the transport of heavy metals. Models with these characteristics are not common to be found elsewhere.
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Cartwright, D. E. "Ocean tides. Mathematical models and numerical experiments." Endeavour 9, no. 2 (January 1985): 109. http://dx.doi.org/10.1016/0160-9327(85)90062-6.
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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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FERRARI, A., L. FRACCAROLLO, M. DUMBSER, E. F. TORO, and A. ARMANINI. "Three-dimensional flow evolution after a dam break." Journal of Fluid Mechanics 663 (October 12, 2010): 456–77. http://dx.doi.org/10.1017/s0022112010003599.
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In this paper, the wave propagation on a plane dry bottom after a dam break is analysed. Two mathematical models have been used and compared with each other for simulating such a dam-break scenario. First, the fully three-dimensional Navier–Stokes equations for a weakly compressible fluid have been solved using the new smooth particle hydrodynamics formulation, recently proposed by Ferrari et al. (Comput. Fluids, vol. 38, 2009, p. 1203). Second, the two-dimensional shallow water equations (SWEs) are solved using a third-order weighted essentially non-oscillatory finite-volume scheme. The numerical results are critically compared against the laboratory measurements provided by Fraccarollo & Toro (J. Hydraul. Res., vol. 33, 1995, p. 843). The experimental data provide the temporal evolution of the pressure field, the water depth and the vertical velocity profile at 40 gauges, located in the reservoir and in front of the gate. Our analysis reveals the shortcomings of SWEs in the initial stages of the dam-break phenomenon in reproducing many important flow features of the unsteady free-surface flow: the shallow water model predicts a complex wave structure and a wavy evolution of local free-surface elevations in the reservoir that can be clearly identified to be only model artefacts. However, the quasi-incompressible Navier–Stokes model reproduces well the high gradients in the flow field and predicts the cycles of simultaneous rapid decreasing and frozen stages of the free surface in the tank along with the velocity oscillations. Asymptotically, i.e. for ‘large times’, the shallow water model and the weakly compressible Navier–Stokes model agree well with the experimental data, since the classical SWE assumptions are satisfied only at large times.
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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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Shain, Kenneth H. "Mathematical Models of Cancer Evolution and Cure." Blood 126, no. 23 (December 3, 2015): SCI—55—SCI—55. http://dx.doi.org/10.1182/blood.v126.23.sci-55.sci-55.
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You cannot cure what you do not understand. So how can mathematical modeling address this pressing issue? The advances in therapeutic success in multiple myeloma over the last decades have hinged on an an army of researchers identifying a critical genetic, epigenetic and biochemical signaling factors within of MM cells as well as the tumor microenvironment (TME). Unfortunately, despite these large scale efforts we do not yet offer our patients curative intent therapy. The inability to provide curative therapy, especially in the setting of HRMM, is characterized by evolving resistance to lines of sequential therapy as a result of alternating clonal dynamics following the failure of initial therapy to eradicate minimal residual disease (MRD). Recent results underline the importance of tumor heterogeneity, in the form of pre-existing genotypically (and phenotypically) distinct sub-populations that translate to drug-resistant phenotypes leading to treatment failure. This phenomenon of “clonal tides”, has been well characterized using contemporary molecular techniques demonstrating that clonal evolution progresses by different evolutionary patterns across patients. Thus, resistance to therapy is a consequence of Darwinian dynamics- influenced by tumor heterogeneity, genomic instability, the TME (ecosystem), and selective pressures induced by therapy. Such evolutionary principles can be analyzed and exploited by mathematical models to personalize therapeutic options for patients with MM. Currently available clinical decision support tools and physician acumen are not able to account for the shear amount of information available. Mathematical models, however, provide a critical mechanism(s) to account of the large number of aspects to help predict and manage MM- accounting for what we do not know. Models can be designed with the specific intent of characterizing intra-tumoral heterogeneity, changing ecosystems, and clinical parameters over time to create patient-specific clinical predictions much like hurricane prediction models. This can only be achieved by creating mathematical models parameterized by longitudinal data of a number of parameters. The novel application of mathematical models based on Darwinian dynamics can be imputed with data to 1) predict progression events (risk of progression to from smoldering to active MM), 2) relapse, and 3) predictions of clinical response of MM patients for the optimizing therapeutics for cure or optimal control of MM; thus, providing invaluable clinical decision support tools. Disclosures: Shain: Celgene: Consultancy , Speakers Bureau ; Amgen/Onyx: Consultancy , Speakers Bureau ; Takeda: Consultancy , Speakers Bureau ; Signal Genetics: Consultancy , Research Funding.
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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Willis, David H., and B. G. Krishnappan. "Numerical modelling of cohesive sediment transport in rivers." Canadian Journal of Civil Engineering 31, no. 5 (October 1, 2004): 749–58. http://dx.doi.org/10.1139/l04-043.
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Techniques available to practicing civil engineers for numerically modelling cohesive mud in rivers and estuaries are reviewed. Coupled models, treating water and sediment as a single process, remain research tools but are usually not three-dimensional. The decoupled approach, which separates water and sediment computations at each model time step, allows the three-dimensional representation of at least the bed and the use of well-proven, commercial, numerical, hydrodynamic models. Most hydrodynamic models compute sediment transport in suspension but may require modification of the dispersion coefficients to account for the presence of sediment. The sediment model deals with the sediment exchange between the water column and the bed using existing equations for erosion and deposition. Both equations relate the sediment exchange rates to the shear stress in the bottom boundary layer. In real rivers and estuaries, a depositional bed layer is associated with a period of low flow and shear, at slack tide for example, whereas in numerical models a layer is defined by the model time step. The sediment model keeps track of the uppermost layers at each model grid point, including consolidation and strengthening. Although numerical hydrodynamic models are based strongly on physics, sediment models are only numerical frameworks for interpolating and extrapolating full-scale field or laboratory measurements of "hydraulic sediment parameters," such as threshold shear stresses. Calibration and verification of models against measurement are therefore of prime importance.Key words: cohesive sediment, mathematical modelling, settling velocity, erosion, resuspension, deposition, fluid mud, bed layers.
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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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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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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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Thiébot, Jérôme, D. S. Coles, Anne-Claire Bennis, Nicolas Guillou, Simon Neill, Sylvain Guillou, and Matthew Piggott. "Numerical modelling of hydrodynamics and tidal energy extraction in the Alderney Race: a review." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2178 (July 27, 2020): 20190498. http://dx.doi.org/10.1098/rsta.2019.0498.
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The tides are a predictable, renewable, source of energy that, if harnessed, can provide significant levels of electricity generation. The Alderney Race (AR), with current speeds that exceed 5 m s −1 during spring tides, is one of the most concentrated regions of tidal energy in the world, with the upper-bound resource estimated at 5.1 GW. Owing to its significance, the AR is frequently used for model case studies of tidal energy conversion, and here we review these model applications and outcomes. We examine a range of temporal and spatial modelling scales, from regional models applied to resource assessment and characterization, to more detailed models that include energy extraction and array optimization. We also examine a range of physical processes that influence the tidal energy resource, including the role of waves and turbulence in tidal energy resource assessment and loadings on turbines. The review discusses model validation, and covers a range of numerical modelling approaches, from two-dimensional to three-dimensional tidal models, two-way coupled wave-tide models, Large Eddy Simulation (LES) models, and the application of optimization techniques. The review contains guidance on model approaches and sources of data that can be used for future studies of the AR, or translated to other tidal energy regions. This article is part of the theme issue ‘New insights on tidal dynamics and tidal energy harvesting in the Alderney Race’.
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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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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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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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Yu, Feng, and Yong Yin. "Oil Spill Visualization Based on the Numeric Simulation of Tidal Current." International Journal of Virtual Reality 8, no. 2 (January 1, 2009): 71–74. http://dx.doi.org/10.20870/ijvr.2009.8.2.2727.
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This paper proposes an approach to implement the 3D visualization of oil spill based on tidal hydrodynamic model. It simulates tidal current of M2 component tide in Jiaozhou Bay. The simulation results conform to the tidal theory and probably conform to the flow measurement report of crude oil pier Phase III at Qingdao Harbor. Based on tidal current and eye-point related adaptive ocean surface mesh model, by analyzing the drift and diffusion mathematical models of oil spill on the sea, the dynamic visualization of drift and diffusion course of oil on the sea were implemented, the visualization result is satisfactory.
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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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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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Abdul Salam, Parveena Shamim, Wolfgang Bock, Axel Klar, and Sudarshan Tiwari. "Disease contagion models coupled to crowd motion and mesh-free simulation." Mathematical Models and Methods in Applied Sciences 31, no. 06 (April 9, 2021): 1277–95. http://dx.doi.org/10.1142/s0218202521400066.
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Modeling and simulation of disease spreading in pedestrian crowds have recently become a topic of increasing relevance. In this paper, we consider the influence of the crowd motion in a complex dynamical environment on the course of infection of the pedestrians. To model the pedestrian dynamics, we consider a kinetic equation for multi-group pedestrian flow based on a social force model coupled with an Eikonal equation. This model is coupled with a non-local SEIS contagion model for disease spread, where besides the description of local contacts, the influence of contact times has also been modeled. Hydrodynamic approximations of the coupled system are derived. Finally, simulations of the hydrodynamic model are carried out using a mesh-free particle method. Different numerical test cases are investigated, including uni- and bi-directional flow in a passage with and without obstacles.
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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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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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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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Iz, H. Bâki, T. Y. Yang, C. K. Shum, and C. Y. Kuo. "Optimal mathematical and statistical models to estimate vertical crustal movements using satellite altimetry and tide gauge data." Journal of Geodetic Science 9, no. 1 (January 1, 2019): 144–53. http://dx.doi.org/10.1515/jogs-2019-0014.
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Abstract Knowledge of vertical crustal movement is fundamental to quantify absolute sea level changes at tide gauge locations as well as for satellite altimetry calibration validations. While GPS measurements at collocated tide gauge stations fulfill this need, currently only few hundred tide gauge stations are equipped with GPS, and their measurements do not span a long period of time. In the past, several studies addressed this problem by calculating relative and geocentric trends from the tide gauge and satellite altimetry measurements respectively, and then difference the two trends to calculate the rate of changes at the tide gauge stations. However, this approach is suboptimal. This study offers an optimal statistical protocol based on the method of condition equations with unknown parameters. An example solution demonstrates the proposed mathematical and statistical models’ optimality in estimating vertical crustal movement and its standard error by comparing them with the results of current methods. The proposed model accounts for the effect of autocorrelations in observed tide gauge and satellite altimetry sea level time series, adjusts observed corrections such as inverted barometer effects, and constraints tide gauge and satellite altimeter measurement to close. The new model can accommodate estimating other systematic effects such as pole tides that are not eliminated by differencing.
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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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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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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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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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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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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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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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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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Carrillo, José A., Aneta Wróblewska-Kamińska, and Ewelina Zatorska. "On long-time asymptotics for viscous hydrodynamic models of collective behavior with damping and nonlocal interactions." Mathematical Models and Methods in Applied Sciences 29, no. 01 (January 2019): 31–63. http://dx.doi.org/10.1142/s0218202519500027.
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Hydrodynamic systems arising in swarming modeling include nonlocal forces in the form of attractive–repulsive potentials as well as pressure terms modeling strong local repulsion. We focus on the case where there is a balance between nonlocal attraction and local pressure in presence of confinement in the whole space. Under suitable assumptions on the potentials and the pressure functions, we show the global existence of weak solutions for the hydrodynamic model with viscosity and linear damping. By introducing linear damping in the system, we ensure the existence and uniqueness of stationary solutions with compactly supported density, fixed mass and center of mass. The associated velocity field is zero in the support of the density. Moreover, we show that global weak solutions converge for large times to the set of these stationary solutions in a suitable sense. In particular cases, we can identify the limiting density uniquely as the global minimizer of the free energy with the right mass and center of mass.