Статті в журналах: "Fluid-structure interaction – Mathematical models"

1

Griffith, Boyce E., and Neelesh A. Patankar. "Immersed Methods for Fluid–Structure Interaction." Annual Review of Fluid Mechanics 52, no. 1 (January 5, 2020): 421–48. http://dx.doi.org/10.1146/annurev-fluid-010719-060228.

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Fluid–structure interaction is ubiquitous in nature and occurs at all biological scales. Immersed methods provide mathematical and computational frameworks for modeling fluid–structure systems. These methods, which typically use an Eulerian description of the fluid and a Lagrangian description of the structure, can treat thin immersed boundaries and volumetric bodies, and they can model structures that are flexible or rigid or that move with prescribed deformational kinematics. Immersed formulations do not require body-fitted discretizations and thereby avoid the frequent grid regeneration that can otherwise be required for models involving large deformations and displacements. This article reviews immersed methods for both elastic structures and structures with prescribed kinematics. It considers formulations using integral operators to connect the Eulerian and Lagrangian frames and methods that directly apply jump conditions along fluid–structure interfaces. Benchmark problems demonstrate the effectiveness of these methods, and selected applications at Reynolds numbers up to approximately 20,000 highlight their impact in biological and biomedical modeling and simulation.

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2

Benaroya, Haym, and Rene D. Gabbai. "Modelling vortex-induced fluid–structure interaction." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1868 (November 5, 2007): 1231–74. http://dx.doi.org/10.1098/rsta.2007.2130.

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The principal goal of this research is developing physics-based, reduced-order, analytical models of nonlinear fluid–structure interactions associated with offshore structures. Our primary focus is to generalize the Hamilton's variational framework so that systems of flow-oscillator equations can be derived from first principles. This is an extension of earlier work that led to a single energy equation describing the fluid–structure interaction. It is demonstrated here that flow-oscillator models are a subclass of the general, physical-based framework. A flow-oscillator model is a reduced-order mechanical model, generally comprising two mechanical oscillators, one modelling the structural oscillation and the other a nonlinear oscillator representing the fluid behaviour coupled to the structural motion. Reduced-order analytical model development continues to be carried out using a Hamilton's principle-based variational approach. This provides flexibility in the long run for generalizing the modelling paradigm to complex, three-dimensional problems with multiple degrees of freedom, although such extension is very difficult. As both experimental and analytical capabilities advance, the critical research path to developing and implementing fluid–structure interaction models entails formulating generalized equations of motion, as a superset of the flow-oscillator models; and developing experimentally derived, semi-analytical functions to describe key terms in the governing equations of motion. The developed variational approach yields a system of governing equations. This will allow modelling of multiple d.f. systems. The extensions derived generalize the Hamilton's variational formulation for such problems. The Navier–Stokes equations are derived and coupled to the structural oscillator. This general model has been shown to be a superset of the flow-oscillator model. Based on different assumptions, one can derive a variety of flow-oscillator models.

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3

Surana, K. S., B. Blackwell, M. Powell, and J. N. Reddy. "Mathematical models for fluid–solid interaction and their numerical solutions." Journal of Fluids and Structures 50 (October 2014): 184–216. http://dx.doi.org/10.1016/j.jfluidstructs.2014.06.023.

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4

Lopes, D., H. Puga, J. C. Teixeira, and S. F. Teixeira. "Fluid–Structure Interaction study of carotid blood flow: Comparison between viscosity models." European Journal of Mechanics - B/Fluids 83 (September 2020): 226–34. http://dx.doi.org/10.1016/j.euromechflu.2020.05.010.

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5

Marom, Gil. "Numerical Methods for Fluid–Structure Interaction Models of Aortic Valves." Archives of Computational Methods in Engineering 22, no. 4 (October 2, 2014): 595–620. http://dx.doi.org/10.1007/s11831-014-9133-9.

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6

Tello, Alexis, Ramon Codina, and Joan Baiges. "Fluid structure interaction by means of variational multiscale reduced order models." International Journal for Numerical Methods in Engineering 121, no. 12 (February 27, 2020): 2601–25. http://dx.doi.org/10.1002/nme.6321.

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7

Larsson, Jonas. "A new Hamiltonian formulation for fluids and plasmas. Part 2. MHD models." Journal of Plasma Physics 55, no. 2 (April 1996): 261–78. http://dx.doi.org/10.1017/s0022377800018821.

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The new Hamiltonian formulation of the perfect fluid equations presented in part 1 of this series of papers is generalized to a class of IVIHD models, including for example ideal MHD and the Chew–Goldberger–Low equations. The mathematical structure is to a great extent unchanged by this generalization, and most results about the small-amplitude expansion of the perfect fluid equations remain obviously valid. For example, we now have a rigorous proof of the Manley-Rowe relations in resonant three-wave interaction, valid for this class of MHD models and for quite general inhomogeneous but stationary background states, including equilibrium flows.

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8

Cottet, Georges-Henri, Emmanuel Maitre, and Thomas Milcent. "Eulerian formulation and level set models for incompressible fluid-structure interaction." ESAIM: Mathematical Modelling and Numerical Analysis 42, no. 3 (April 3, 2008): 471–92. http://dx.doi.org/10.1051/m2an:2008013.

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9

Desjardins, B., and M. J. Esteban. "On Weak Solutions for Fluid‐Rigid Structure Interaction: Compressible and Incompressible Models." Communications in Partial Differential Equations 25, no. 7-8 (January 1999): 263–85. http://dx.doi.org/10.1080/03605300008821553.

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10

Colciago, C. M., S. Deparis, and A. Quarteroni. "Comparisons between reduced order models and full 3D models for fluid–structure interaction problems in haemodynamics." Journal of Computational and Applied Mathematics 265 (August 2014): 120–38. http://dx.doi.org/10.1016/j.cam.2013.09.049.

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11

Lara, Javier L., Inigo J. Losada, Gabriel Barajas, Maria Maza, and Benedetto Di Paolo. "RECENT ADVANCES IN 3D MODELLING OF WAVE-STRUCTURE INTERACTION WITH CFD MODELS." Coastal Engineering Proceedings, no. 36 (December 30, 2018): 91. http://dx.doi.org/10.9753/icce.v36.waves.91.

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Numerical modelling of the interaction of water waves with coastal structures has continuously been among the most relevant challenges in coastal engineering research and practice. During the last years, 3D modelling based on RANS-type equations, has been the dominant methodology to address the mathematical modelling of wave and coastal structure interaction. However, the three-dimensionality of many flowstructure interactions processes demands overcoming existing modelling limitations. Under some circumstances relevant three-dimensional processes are still tackled using physical modelling. It has been shown that beyond numerical implementation of the well-known mathematical 3-D formulation of the Navier-Stokes equations, the application of 3-D codes to standard coastal engineering problems demands some additional steps to be taken. These steps could be classified into three main groups relevant to: a) the modelling of the physical processes; b) the use of the tool and c) the applicability of the codes. This work presents an analysis of the use of three-dimensional flow models to analyze wave interaction with coastal structures focusing on recent developments overcoming existing limitations. Last modelling advances, including the implementation of new physics and pre-and postprocessing tools will be shown with the aim of extending the use of three-dimensional modelling of wavestructure interaction in both coastal and offshore fields.

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12

Tang, Aik Ying, and Norsarahaida Amin. "Some Numerical Approaches to Solve Fluid Structure Interaction Problems in Blood Flow." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/549189.

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Some numerical approaches to solve fluid structure interaction problems in blood flow are reviewed. Fluid structure interaction is the interaction between a deformable structure with either an internal or external flow. A discussion on why the compliant artery associated with fluid structure interaction should be taken into consideration in favor of the rigid wall model being included. However, only the Newtonian model of blood is assumed, while various structure models which include, amongst others, generalized string models and linearly viscoelastic Koiter shell model that give a more realistic representation of the vessel walls compared to the rigid structure are presented. Since there exists a strong added mass effect due to the comparable densities of blood and the vessel wall, the numerical approaches to overcome the added mass effect are discussed according to the partitioned and monolithic classifications, where the deficiencies of each approach are highlighted. Improved numerical methods which are more stable and offer less computational cost such as the semi-implicit, kinematic splitting, and the geometrical multiscale approach are summarized, and, finally, an appropriate structure and numerical scheme to tackle fluid structure interaction problems are proposed.

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13

Ballarin, Francesco, and Gianluigi Rozza. "POD-Galerkin monolithic reduced order models for parametrized fluid-structure interaction problems." International Journal for Numerical Methods in Fluids 82, no. 12 (June 21, 2016): 1010–34. http://dx.doi.org/10.1002/fld.4252.

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14

Kamenskiy, Alexey V., Iraklis I. Pipinos, Yuris A. Dzenis, Prateek K. Gupta, Syed A. Jaffar Kazmi, and Jason N. MacTaggart. "A mathematical evaluation of hemodynamic parameters after carotid eversion and conventional patch angioplasty." American Journal of Physiology-Heart and Circulatory Physiology 305, no. 5 (September 1, 2013): H716—H724. http://dx.doi.org/10.1152/ajpheart.00034.2013.

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Carotid endarterectomy has a long history in stroke prevention, yet controversy remains concerning optimal techniques. Two methods frequently used are endarterectomy with patch angioplasty (CEAP) and eversion endarterectomy (CEE). The objective of this study was to compare hemodynamics-related stress and strain distributions between arteries repaired using CEAP and CEE. Mathematical models were based on in vivo three-dimensional arterial geometry, pulsatile velocity profiles, and intraluminal pressure inputs obtained from 16 patients with carotid artery disease. These data were combined with experimentally derived nonlinear, anisotropic carotid artery mechanical properties to create fluid-structure interaction models of CEAP and CEE. These models were then used to calculate hemodynamic parameters thought to promote recurrent disease and restenosis. Combining calculations of stress and strain into a composite risk index, called the integral abnormality factor, allowed for an overall comparison between CEAP and CEE. CEE demonstrated lower mechanical stresses in the arterial wall, whereas CEAP straightened the artery and caused high stress and strain concentrations at the suture-artery interface. CEAP produced a larger continuous region of oscillatory, low-shear, vortical flow in the carotid bulb. There was a more than two-fold difference in the integral abnormality factor, favoring CEE. In conclusion, in a realistically simulated carotid artery, fluid-structure interaction modeling demonstrated CEE to produce less mechanical wall stress and improved flow patterns compared with CEAP. Clinical validation with larger numbers of individual patients will ultimately be required to support modeling approaches to help predict arterial disease progression and comparative effectiveness of reconstruction methods and devices.

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15

Wang, Xiaojing, Guojia Man, and Mengjian Zhang. "Research on the leakage of continuous rotary electro-hydraulic servo motor based on fluid structure interaction analysis." Industrial Lubrication and Tribology 70, no. 3 (April 9, 2018): 544–51. http://dx.doi.org/10.1108/ilt-03-2017-0064.

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Purpose Internal leakage is one of the key factors that influence the super-low speed performance of continuous rotary electro-hydraulic servo motor. Therefore, this paper aims to study the change rule of internal leakage for improving the low speed performance of motor. Design/methodology/approach The mathematical models of internal leakage of continuous rotary electro-hydraulic servo motor were established, and according to the working principle of the motor, the 3D models of internal leakage location were established. Simulation analysis was implemented on the continuous rotary electro-hydraulic servo motor by the finite element analysis software ANSYS based on the fluid-structure interaction theory. Findings The results show the deformation of motor’s key parts and the changing rule of internal leakage. The effect of the leakage to the low speed performance of electro-hydraulic servo motor was analyzed, and at the same time, the motor’s leakage experiment was also conducted to verify the validity of simulation results. Originality/value This paper lays the foundation for improving the low speed performance of motor.

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16

Weinstein, Alan M. "Mathematical models of renal fluid and electrolyte transport: acknowledging our uncertainty." American Journal of Physiology-Renal Physiology 284, no. 5 (May 1, 2003): F871—F884. http://dx.doi.org/10.1152/ajprenal.00330.2002.

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Mathematical models of renal tubular function, with detail at the cellular level, have been developed for most nephron segments, and these have generally been successful at capturing the overall bookkeeping of solute and water transport. Nevertheless, considerable uncertainty remains about important transport events along the nephron. The examples presented include the role of proximal tubule tight junctions in water transport and in regulation of Na+ transport, the mechanism by which axial flow in proximal tubule modulates solute reabsorption, the effect of formate on proximal Cl− transport, the assessment of potassium transport along collecting duct segments inaccessible to micropuncture, the assignment of pathways for peritubular Cl− exit in outer medullary collecting duct, and the interaction of carbonic anhydrase-sensitive and -insensitive pathways for base exit from inner medullary collecting duct. Some of these uncertainties have had intense experimental interest well before they were cast as modeling problems. Indeed, many of the renal tubular models have been developed based on data acquired over two or three decades. Nevertheless, some uncertainties have been delineated as the result of model exploration and represent communications from the modelers back to the experimental community that certain issues should not be considered closed. With respect to model refinement, incorporating more biophysical detail about individual transporters will certainly enhance model reliability, but ultimate confidence in tubular models will still be contingent on experimental development of critical information at the tubular level.

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17

Chen, Mingqiang, Linsong Cheng, Renyi Cao, and Chaohui Lyu. "A Study to Investigate Fluid-Solid Interaction Effects on Fluid Flow in Micro Scales." Energies 11, no. 9 (August 22, 2018): 2197. http://dx.doi.org/10.3390/en11092197.

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Due to micro-nanopores in tight formation, fluid-solid interaction effects on fluid flow in porous media cannot be ignored. In this paper, a novel model which can characterize micro-fluid flow in micro scales is proposed. This novel model has a more definite physical meaning compared with other empirical models. And it is validated by micro tube experiments. In addition, the application range of the model is rigorously analyzed from a mathematical view, which indicates a wider application scope. Based on the novel model, the velocity profile, the average flow velocity and flow resistance in consideration of fluid-solid interaction are obtained. Furthermore, the novel model is incorporated into a representative pore scale network model to study fluid-solid interactions on fluid flow in porous media. Results show that due to fluid-solid interaction in micro scales, the change rules of the velocity profile, the average flow velocity and flow resistance generate obvious deviations from traditional Hagen-Poiseuille’s law. The smaller the radius and the lower the displacement pressure gradient (∇P), the more obvious the deviations will be. Moreover, the apparent permeability in consideration of fluid-solid interaction is no longer a constant, it increases with the increase of ∇P and non-linear flow appears at low ∇P. This study lays a good foundation for studying fluid flow in tight formation.

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18

Colicchio, G., M. Greco, M. Brocchini, and O. M. Faltinsen. "Hydroelastic behaviour of a structure exposed to an underwater explosion." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373, no. 2033 (January 28, 2015): 20140103. http://dx.doi.org/10.1098/rsta.2014.0103.

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The hydroelastic interaction between an underwater explosion and an elastic plate is investigated num- erically through a domain-decomposition strategy. The three-dimensional features of the problem require a large computational effort, which is reduced through a weak coupling between a one-dimensional radial blast solver, which resolves the blast evolution far from the boundaries, and a three-dimensional compressible flow solver used where the interactions between the compression wave and the boundaries take place and the flow becomes three-dimensional. The three-dimensional flow solver at the boundaries is directly coupled with a modal structural solver that models the response of the solid boundaries like elastic plates. This enables one to simulate the fluid–structure interaction as a strong coupling, in order to capture hydroelastic effects. The method has been applied to the experimental case of Hung et al. (2005 Int. J. Impact Eng. 31 , 151–168 ( doi:10.1016/j.ijimpeng.2003.10.039 )) with explosion and structure sufficiently far from other boundaries and successfully validated in terms of the evolution of the acceleration induced on the plate. It was also used to investigate the interaction of an underwater explosion with the bottom of a close-by ship modelled as an orthotropic plate. In the application, the acoustic phase of the fluid–structure interaction is examined, highlighting the need of the fluid–structure coupling to capture correctly the possible inception of cavitation.

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19

Sadeghi, J., M. Khurshudyan, and H. Farahani. "Interacting ghost dark energy models in the higher dimensional cosmology." International Journal of Modern Physics D 25, no. 14 (December 2016): 1650108. http://dx.doi.org/10.1142/s021827181650108x.

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We investigate interacting ghost dark energy models in higher dimensional cosmology. We attempt to model dark matter within a barotropic fluid with [Formula: see text]. In this work, we consider four different models based on choosing equation of state (EoS) parameter and interaction term. We confirm that our models agree with observational data.

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20

Bouaanani, Najib, Patrick Paultre, and Jean Proulx. "Dynamic response of a concrete dam impounding an ice-covered reservoir: Part I. Mathematical modelling." Canadian Journal of Civil Engineering 31, no. 6 (December 1, 2004): 956–64. http://dx.doi.org/10.1139/l04-075.

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This paper examines the dynamic response of a concrete dam impounding an ice-covered reservoir and subjected to forced-vibration testing. The analytical research presented is a follow-up to an extensive dynamic testing program carried out on a 84-m high concrete gravity dam located in northeastern Quebec, Canada, under harsh winter conditions, including a 1.0- to 1.5-m-thick ice sheet covering the reservoir. One of the major challenges encountered when analyzing ice-dam-reservoir-foundation interaction is modelling the complex nature of the ice and the boundary conditions governing reservoir motion. The problem is further complicated because there are little or no appropriate experimental data and observational evidence relevant to ice-dam interaction processes. Some of these challenges are addressed herein using a two-dimensional analytical approach, which investigates the effects due to ice cover, water compressibility, and reservoir bottom absorption. A frequency-domain substructure method technique is used and a new boundary condition along the ice-cover-reservoir interface is proposed. The technique developed is implemented in a finite element code specialized in the seismic analysis of concrete dams. Numerical results are discussed in the companion paper in this issue. Key words: gravity dams, concrete dams, ice, reservoirs, mathematical models, ice-structure interaction, fluid-structure interaction, forced-vibration testing, finite elements modelling.

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21

Jiang, Qinglei, Lulu Zhai, Leqin Wang, and Dazhuan Wu. "Fluid-Structure Interaction Analysis on Turbulent Annular Seals of Centrifugal Pumps during Transient Process." Mathematical Problems in Engineering 2011 (2011): 1–22. http://dx.doi.org/10.1155/2011/929574.

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The current paper studies the influence of annular seal flow on the transient response of centrifugal pump rotors during the start-up period. A single rotor system and three states of annular seal flow were modeled. These models were solved using numerical integration and finite difference methods. A fluid-structure interaction method was developed. In each time step one of the three annular seal models was chosen to simulate the annular seal flow according to the state of rotor systems. The objective was to obtain a transient response of rotor systems under the influence of fluid-induced forces generated by annular seal flow. This method overcomes some shortcomings of the traditional FSI method by improving the data transfer process between two domains. Calculated results were in good agreement with the experimental results. The annular seal was shown to have a supportive effect on rotor systems. Furthermore, decreasing the seal clearance would enhance this supportive effect. In the transient process, vibration amplitude and critical speed largely changed when the acceleration of the rotor system increased.

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22

Drobakha, Hr, I. Neklonskyi, A. Kateshchenok, V. Sobyna, D. Taraduda, L. Borysova, and I. Lysachenko. "Structural and functional simulation of interaction in the field of aviation safety by using matrices." Archives of Materials Science and Engineering 2, no. 95 (February 1, 2019): 74–84. http://dx.doi.org/10.5604/01.3001.0013.1734.

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Purpose: The conducted research was aimed at constructing a structural and functional model for the interaction of bodies providing aviation safety during crisis management. Design/methodology/approach: The methods of mathematical simulation and the graph theory, the methods comparison and formalization have been applied to study the process of interaction between the bodies assuring aviation safety. Using methods of the linear algebra allowed constructing a mathematical model for the functional structure of the interaction process that contains description of this process by the main methods of interaction. Findings: It has been proved that the interaction process has a certain functional properties that reflect the functional relations between the modes of violator actions, the modes of using the response forces and the modes of interaction. A structural and functional model of interaction in semantic, algebraic forms and in the form of graphs has been created. using typical operations with incidence matrices, the possibility of obtaining the physical interpretation of the simulation results within the introduced algebra of functional structure models has been justified. Research limitations/implications: Discusses interactions between the bodies that assure aviation safety and at the same time, the possibility of a crisis situation is taken into account. Practical implications: The developed models allow reflecting the current state of the functional system and the elements of the process of interaction rather completely. It makes a structural and functional analysis of interaction possible and allows defining the priority directions of its organization, simulating the options and methods of interaction in solving relevant tasks by the bodies that assure aviation safety. Originality/value: That allowed not only describing the formal relations between the methods of interaction and interacting units, between the interacting units and the modes of violator actions, but also considering the influence of the interaction process on the current state of the functional system.

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23

Ellam, L., M. Girolami, G. A. Pavliotis, and A. Wilson. "Stochastic modelling of urban structure." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2213 (May 2018): 20170700. http://dx.doi.org/10.1098/rspa.2017.0700.

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The building of mathematical and computer models of cities has a long history. The core elements are models of flows (spatial interaction) and the dynamics of structural evolution. In this article, we develop a stochastic model of urban structure to formally account for uncertainty arising from less predictable events. Standard practice has been to calibrate the spatial interaction models independently and to explore the dynamics through simulation. We present two significant results that will be transformative for both elements. First, we represent the structural variables through a single potential function and develop stochastic differential equations to model the evolution. Second, we show that the parameters of the spatial interaction model can be estimated from the structure alone, independently of flow data, using the Bayesian inferential framework. The posterior distribution is doubly intractable and poses significant computational challenges that we overcome using Markov chain Monte Carlo methods. We demonstrate our methodology with a case study on the London, UK, retail system.

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24

Falahati, M., and M. Behdarvandi Askar. "Seismic Performance of the Pier Considering Structural-Fluid Interaction with ANSYS Software." Journal of Applied Engineering Sciences 7, no. 2 (December 1, 2017): 25–30. http://dx.doi.org/10.1515/jaes-2017-0009.

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Abstract In the present study, as the calculation of forces on the cylindrical structures of the sea has a special complexity, Morrison's mathematical model was used in the software. In addition, the kinematics of water particles is estimated to calculate their acceleration from the fifth-order non-static wave theory (Fenton method). In this paper, the analysis of the pier performance considering structural-fluid interaction using ANSYS soft is presented. Five models with the same period were considered and different wave heights and two different earthquake records of Tabas and Northwich were studied. Finally, node displacement, acceleration and reciprocal interaction forces were extracted and compared with the numerical values. The results indicated that the values of the studied parameters and the type of nodes were similar in the models without a record of earthquakes, but with the estimation of the earthquake, these values would be significant.

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25

Petruk, O. O., O. T. Vavryk, O. S. Tsareva, and L. M. Hobyr. "MODEL REPRESENTATIONS OF THE MELTS STRUCTURE DESCRIPTION BY THE MODEL OF HARD SPHERES." PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY Number, no. 1(59) (January 28, 2021): 72–78. http://dx.doi.org/10.31471/2304-7399-2020-1(59)-72-78.

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In the article the optimization of the oil and gas enterprise, a complex process both from the technological and from the economic point of view is investigated. It is noted that today the development of methods of mathematical modeling of physical processes, for example, in oil fields on the basis of theoretical research and modern computer technology is absolutely relevant One of the ways is to create new or improve existing mathematical models of processes occurring in oil and gas reservoirs, and calculate on their basis the characteristics of the process that optimize production. From this perspective, the study appears particularly relevant liquids in a narrow, purely physical and chemical aspects – namely melt. Various fluid models have been proposed to describe the equilibrium and kinetic properties of liquids (melts), as well as to interpret experimental results. Model representations are also used in solving integrodifferential equations that relate distribution functions to interaction potentials. It is noted that integrodifferential equations are a powerful mathematical algorithm for describing inhomogeneous dynamic models, but they depend directly on the efficiency of software that implements the proposed models. The model of hard spheres as simple fluid model proposed use. The reasons that allow you to choose this model as optimal were defined. Namely: the presence of analytical expression for the structural factor; application to describe the electronic and atomic properties of melts. The optimal methods for obtaining optimal values for the theoretical calculation of the structural factor of the proposed model were determined. As a result of the analysis of existence of correspondence between the calculated and experimental structural factors it is established. This led to the conclusion that the possibility of applying the model of rigid to calculate the equilibrium and kinetic properties of melts exists. It is determined that the model of rigid spheres could be used as an approximation to describe the structure of both one-component and multicomponential melts (liquids).

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26

Laugesen, Jakob L., Olga V. Sosnovtseva, Erik Mosekilde, Niels-Henrik Holstein-Rathlou, and Donald J. Marsh. "Coupling-induced complexity in nephron models of renal blood flow regulation." American Journal of Physiology-Regulatory, Integrative and Comparative Physiology 298, no. 4 (April 2010): R997—R1006. http://dx.doi.org/10.1152/ajpregu.00714.2009.

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Tubular pressure and nephron blood flow time series display two interacting oscillations in rats with normal blood pressure. Tubuloglomerular feedback (TGF) senses NaCl concentration in tubular fluid at the macula densa, adjusts vascular resistance of the nephron's afferent arteriole, and generates the slower, larger-amplitude oscillations (0.02–0.04 Hz). The faster smaller oscillations (0.1–0.2 Hz) result from spontaneous contractions of vascular smooth muscle triggered by cyclic variations in membrane electrical potential. The two mechanisms interact in each nephron and combine to act as a high-pass filter, adjusting diameter of the afferent arteriole to limit changes of glomerular pressure caused by fluctuations of blood pressure. The oscillations become irregular in animals with chronic high blood pressure. TGF feedback gain is increased in hypertensive rats, leading to a stronger interaction between the two mechanisms. With a mathematical model that simulates tubular and arteriolar dynamics, we tested whether an increase in the interaction between TGF and the myogenic mechanism can cause the transition from periodic to irregular dynamics. A one-dimensional bifurcation analysis, using the coefficient that couples TGF and the myogenic mechanism as a bifurcation parameter, shows some regions with chaotic dynamics. With two nephrons coupled electrotonically, the chaotic regions become larger. The results support the hypothesis that increased oscillator interactions contribute to the transition to irregular fluctuations, especially when neighboring nephrons are coupled, which is the case in vivo.

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27

Zhekov, Svetozar A., A. V. Myasnikov, and N. A. Belov. "Radiative colliding winds models: the stagnation point singularity." Symposium - International Astronomical Union 193 (1999): 402. http://dx.doi.org/10.1017/s0074180900205949.

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The singularity at the stagnation point in steady-state colliding winds has a big influence on the structure of the radiative interaction region. None of the existing numerical models treats properly this mathematical problem. As a result, all the available models cannot be used for deriving the stellar winds parameters by making a comparison with the observed X-ray properties.

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Bayly, P. V., and S. K. Dutcher. "Steady dynein forces induce flutter instability and propagating waves in mathematical models of flagella." Journal of The Royal Society Interface 13, no. 123 (October 2016): 20160523. http://dx.doi.org/10.1098/rsif.2016.0523.

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Cilia and flagella are highly conserved organelles that beat rhythmically with propulsive, oscillatory waveforms. The mechanism that produces these autonomous oscillations remains a mystery. It is widely believed that dynein activity must be dynamically regulated (switched on and off, or modulated) on opposite sides of the axoneme to produce oscillations. A variety of regulation mechanisms have been proposed based on feedback from mechanical deformation to dynein force. In this paper, we show that a much simpler interaction between dynein and the passive components of the axoneme can produce coordinated, propulsive oscillations. Steady, distributed axial forces, acting in opposite directions on coupled beams in viscous fluid, lead to dynamic structural instability and oscillatory, wave-like motion. This ‘flutter’ instability is a dynamic analogue to the well-known static instability, buckling. Flutter also occurs in slender beams subjected to tangential axial loads, in aircraft wings exposed to steady air flow and in flexible pipes conveying fluid. By analysis of the flagellar equations of motion and simulation of structural models of flagella, we demonstrate that dynein does not need to switch direction or inactivate to produce autonomous, propulsive oscillations, but must simply pull steadily above a critical threshold force.

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Rejniak, Katarzyna A., and Lisa J. McCawley. "Current trends in mathematical modeling of tumor–microenvironment interactions: a survey of tools and applications." Experimental Biology and Medicine 235, no. 4 (April 2010): 411–23. http://dx.doi.org/10.1258/ebm.2009.009230.

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In its simplest description, a tumor is comprised of an expanding population of transformed cells supported by a surrounding microenvironment termed the tumor stroma. The tumor microcroenvironment has a very complex composition, including multiple types of stromal cells, a dense network of various extracellular matrix (ECM) fibers interpenetrated by the interstitial fluid and gradients of several chemical species that either are dissolved in the fluid or are bound to the ECM structure. In order to study experimentally such complex interactions between multiple players, cancer is dissected and considered at different scales of complexity, such as protein interactions, biochemical pathways, cellular functions or whole organism studies. However, the integration of information acquired from these studies into a common description is as difficult as the disease itself. Computational models of cancer can provide cancer researchers with invaluable tools that are capable of integrating the complexity into organizing principles as well as suggesting testable hypotheses. We will focus in this Minireview on mathematical models in which the whole cell is a main modeling unit. We will present a current stage of such cell-focused mathematical modeling incorporating different stromal components and their interactions with growing tumors, and discuss what modeling approaches can be undertaken to complement the in vivo and in vitro experimentation.

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30

Schiffer, Andreas, and Vito L. Tagarielli. "The response of rigid plates to blast in deep water: fluid–structure interaction experiments." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2145 (May 9, 2012): 2807–28. http://dx.doi.org/10.1098/rspa.2012.0076.

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Laboratory-scale dynamic experiments are performed in order to explore the one-dimensional response of unsupported rigid plates to loading by exponentially decaying planar shock waves in deep water. Experiments are conducted in a transparent shock tube allowing measurements of plate motion and imparted impulse, as well as observation of cavitation in water, including motion of breaking fronts and closing fronts. Loading of both air-backed and water-backed rigid plates is examined, and the sensitivity of plate motion and imparted impulse to the structural mass and to the initial hydrostatic pressure in the water is measured. Experiments also serve to validate recently developed theoretical models, whose predictions are found to be in agreement with measurements.

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31

Wang, Na, Akbar Maleki, Mohammad Alhuyi Nazari, Iskander Tlili, and Mostafa Safdari Shadloo. "Thermal Conductivity Modeling of Nanofluids Contain MgO Particles by Employing Different Approaches." Symmetry 12, no. 2 (February 1, 2020): 206. http://dx.doi.org/10.3390/sym12020206.

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The existence of solid-phase nanoparticles remarkably improves the thermal conductivity of the fluids. The enhancement in this property of the nanofluids is affected by different items such as the solid-phase volume fraction and dimensions, temperature, etc. In the current paper, three different mathematical models, including polynomial correlation, Multivariate Adaptive Regression Spline (MARS), and Group Method of Data Handling (GMDH), are applied to forecast the thermal conductivity of nanofluids containing MgO particles. The inputs of the model are the base fluid thermal conductivity, volume concentration, and average dimension of solid-phase, and nanofluids’ temperature. Comparing the proposed models revealed higher confidence of GMDH in estimating the thermal conductivity, which is attributed to its complicated structure and more appropriate consideration of the input’s interaction. The values of R-squared for the correlation, MARS, and GMDH are 0.9949, 0.9952, and 0.9991, respectively. In addition, based on the sensitivity analysis, the effect of thermal conductivity of the base fluid on the overall thermal conductivity of nanofluids is more remarkable compared with the other inputs such as volume fraction, temperature, and dimensions of the particles which are used as the inputs of the models.

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32

Lukkarinen, Jani. "Multi-state Condensation in Berlin–Kac Spherical Models." Communications in Mathematical Physics 373, no. 1 (December 24, 2019): 389–433. http://dx.doi.org/10.1007/s00220-019-03659-2.

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AbstractWe consider the Berlin–Kac spherical model for supercritical densities under a periodic lattice energy function which has finitely many non-degenerate global minima. Energy functions arising from nearest neighbour interactions on a rectangular lattice have a unique minimum, and in that case the supercritical fraction of the total mass condenses to the ground state of the energy function. We prove that for any sufficiently large lattice size this also happens in the case of multiple global minima, although the precise distribution of the supercritical mass and the structure of the condensate mass fluctuations may depend on the lattice size. However, in all of these cases, one can identify a bounded number of degrees of freedom forming the condensate in such a way that their fluctuations are independent from the rest of the fluid. More precisely, the original Berlin–Kac measure may be replaced by a factorized supercritical measure where the condensate and normal fluid degrees of freedom become independent random variables, and the normal fluid part converges to the critical Gaussian free field. The proof is based on a construction of a suitable coupling between the two measures, proving that their Wasserstein distance is small enough for the error in any finite moment of the field to vanish as the lattice size is increased to infinity.

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33

Guerin, Heather Anne L., and Dawn M. Elliott. "The Role of Fiber-Matrix Interactions in a Nonlinear Fiber-Reinforced Strain Energy Model of Tendon." Journal of Biomechanical Engineering 127, no. 2 (November 18, 2004): 345–50. http://dx.doi.org/10.1115/1.1865212.

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The objective of this study was to develop a nonlinear and anisotropic three-dimensional mathematical model of tendon behavior in which the structural components of fibers, matrix, and fiber-matrix interactions are explicitly incorporated and to use this model to infer the contributions of these structures to tendon mechanical behavior. We hypothesized that this model would show that: (i) tendon mechanical behavior is not solely governed by the isotropic matrix and fiber stretch, but is also influenced by fiber-matrix interactions; and (ii) shear fiber-matrix interaction terms will better describe tendon mechanical behavior than bulk fiber-matrix interaction terms. Model versions that did and did not include fiber-matrix interaction terms were applied to experimental tendon stress-strain data in longitudinal and transverse orientations, and the R2 goodness-of-fit was evaluated. This study showed that models that included fiber-matrix interaction terms improved the fit to longitudinal data (RToe2=0.88,RLin2=0.94) over models that only included isotropic matrix and fiber stretch terms (RToe2=0.36,RLin2=0.84). Shear fiber-matrix interaction terms proved to be responsible for the best fit to data and to contribute to stress-strain nonlinearity. The mathematical model of tendon behavior developed in this study showed that fiber-matrix interactions are an important contributor to tendon behavior. The more complete characterization of mechanical behavior afforded by this mathematical model can lead to an improved understanding of structure-function relationships in soft tissues and, ultimately, to the development of tissue-engineered therapies for injury or degeneration.

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34

Dallon, J. C., E. J. Evans, and H. Paul Ehrlich. "A mathematical model of collagen lattice contraction." Journal of The Royal Society Interface 11, no. 99 (October 6, 2014): 20140598. http://dx.doi.org/10.1098/rsif.2014.0598.

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Two mathematical models for fibroblast–collagen interaction are proposed which reproduce qualitative features of fibroblast-populated collagen lattice contraction. Both models are force based and model the cells as individual entities with discrete attachment sites; however, the collagen lattice is modelled differently in each model. In the collagen lattice model, the lattice is more interconnected and formed by triangulating nodes to form the fibrous structure. In the collagen fibre model, the nodes are not triangulated, are less interconnected, and the collagen fibres are modelled as a string of nodes. Both models suggest that the overall increase in stress of the lattice as it contracts is not the cause of the reduced rate of contraction, but that the reduced rate of contraction is due to inactivation of the fibroblasts.

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35

Piwowarczyk, Marek. "Two Models of the Subject–Properties Structure." Axiomathes 30, no. 4 (November 9, 2019): 371–90. http://dx.doi.org/10.1007/s10516-019-09463-w.

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Abstract In the paper I discuss the problem of the nature of the relationship between objects and their properties. There are three contexts of the problem: of comparison, of change and of interaction. Philosophical explanations of facts indicated in the three contexts need reference to properties and to a proper understanding of a relationship between them and their bearers. My aim is to get closer to this understanding with the use of some models but previously I present the substantialist theory of object and shortly argue for its main theses. The two models enabling us the understanding of the subject–properties structure are: the plastic stuff model and the functional model. On the ground of the first a subject is compared to a piece of plastic stuff which is informed by different shapes. Properties are ways how a subject is, they “give” some “figure” to a subject. The core idea of the second model is that essences (performing the role of subjects) are immanent functional laws governing correlations of properties. As such they are similar to mathematical functions which are saturated by values. The relationship between a subject and properties can be grasped by analogy to such a saturation.

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36

Vu-Quoc, L., and M. Olsson. "High-Speed Vehicle Models Based on a New Concept of Vehicle/Structure Interaction Component: Part I—Formulation." Journal of Dynamic Systems, Measurement, and Control 115, no. 1 (March 1, 1993): 140–47. http://dx.doi.org/10.1115/1.2897389.

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High-speed vehicle/structure models constructed based on a new formulation of dynamic interaction between high-speed vehicles and flexible guideways are presented. A basic vehicle/structure interaction model forms a basic building block of complex vehicle/structure models in which lumped-parameter sub-components of the vehicle component (e.g., suspended masses with springs and dashpots) are assembled onto the basic vehicle/structure interaction component. A vertical and an inclined vehicle models are formulated. These vehicle models can serve as yet more advanced building-block models in the hierarchical construction of complex vehicle/structure models. The inclined vehicle model can be used to study the effects of braking of high-speed vehicles of flexible guideways. Fully nonlinear equations of motion of both models are given. Upon introducing approximations to the nonlinear kinematics, mildly nonlinear equations with an unusual mathematical structure are consistently derived. These equations are appropriate for use under realistic working conditions of the system, and are particularly amenable for numerical treatment using a recently proposed class of predictor/corrector algorithms.

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37

Pavlovska, M. O. "BLOOD PRESSURE, HYPOCHONDRIA AND DEPRESSION: MATHEMATICAL MODELS OF RELATIONSHIP." International Medical Journal, no. 4(104) (December 24, 2020): 12–20. http://dx.doi.org/10.37436/2308-5274-2020-4-2.

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Modern clinical diagnostics has standards and medical systems for the diagnosis of hypertension, advanced information technology. Mathematical models of the relationship between systolic blood pressure and psychological indices of hypochondria and depression have been described. Methods of mathematical statistics were applied as follows: factor, cluster, discriminant, regression analyzes, Markov chains, polynomial splines and neural networks, they were implemented in software products, such as NeuroModelDBPM, "Monitoring", VerMed. The presented model of interaction of systolic arterial pressure, Hs−hypochondria, D−depression confirms an importance of these states at an initial stage of arterial hypertension and allows the allocation of four options of psychosomatic relations in patients: organ and system somatic defeats of psychosomatic character, somaticized psychiatric reactions, reactions of exogenous type. It has been shown that disharmonious personality traits, risk factors, disorder of chronobiological structure of blood pressure, left ventricular hypertrophy and its diastolic dysfunction contribute to the formation of nosogeny in hypertension. Their development is hindered by harmonious personality traits, keeping a healthy lifestyle, minimal changes in the chronobiological structure of blood pressure, a slight degree of left ventricular hypertrophy and its diastolic dysfunction. The leading cardiovascular risk factors in patients with hypertension are stress, burdened heredity, low physical activity, carbohydrate abuse, higher education and high socioeconomic status. Nosogeny in hypertension should also be considered as a risk factor, as well as should be taken into account in the stratification of the overall cardiovascular risk and accomplishing a proper adjustments. Key words: arterial hypertension, mathematical statistics, arterial pressure, hypochondria, depression, information technology.

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38

Cao, Yihua, Shuai Nie, and Zhenlong Wu. "Numerical simulation of parachute inflation: A methodological review." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233, no. 2 (May 12, 2017): 736–66. http://dx.doi.org/10.1177/0954410017705900.

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The parachute inflation process involves fluid–structure interaction problems posing several mathematical and engineering challenges, e.g. accurate aerodynamics calculations for bluff-body geometries involving with moving boundary, appropriate structural models in predicting the behavior of canopy, and realization of the coupling between the fluid and structure. These challenges attract the attention of scholars worldwide, and considerable achievements have been obtained in applying numerical methods and simulations to design multifarious parachutes. In this paper, the authors highlight the advances in the following fields: the methods suitable for time-dependent flow around bluff-body geometries, the accurate structural models in consideration of the under-constrained and no-compression nature of the canopy, and the advantages and disadvantages of different coupling algorithms in terms of numerical stability and computational economics. Moreover, in order to simulate the parachute inflation more realistically, we focus on accurate representation of three physical phenomena, as follows: an appropriate model of the flow through porous media, an accurate treatment of the wrinkling phenomenon of the canopy, and a consistent representation of the impact-contact problem associated with the inflation process. Finally, based on a review of existing literature, we offer recommendations for future research on the application of numerical methods for simulating the inflation process.

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39

GRIFFITH, BOYCE E., XIAOYU LUO, DAVID M. McQUEEN, and CHARLES S. PESKIN. "SIMULATING THE FLUID DYNAMICS OF NATURAL AND PROSTHETIC HEART VALVES USING THE IMMERSED BOUNDARY METHOD." International Journal of Applied Mechanics 01, no. 01 (March 2009): 137–77. http://dx.doi.org/10.1142/s1758825109000113.

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The immersed boundary method is both a general mathematical framework and a particular numerical approach to problems of fluid-structure interaction. In the present work, we describe the application of the immersed boundary method to the simulation of the fluid dynamics of heart valves, including a model of a natural aortic valve and a model of a chorded prosthetic mitral valve. Each valve is mounted in a semi-rigid flow chamber. In the case of the mitral valve, the flow chamber is a circular pipe, and in the case of the aortic valve, the flow chamber is a model of the aortic root. The model valves and flow chambers are immersed in a viscous incompressible fluid, and realistic fluid boundary conditions are prescribed at the upstream and downstream ends of the chambers. To connect the immersed boundary models to the boundaries of the fluid domain, we introduce a novel modification of the standard immersed boundary scheme. In particular, near the outer boundaries of the fluid domain, we modify the construction of the regularized delta function which mediates fluid-structure coupling in the immersed boundary method, whereas in the interior of the fluid domain, we employ a standard four-point delta function which is frequently used with the immersed boundary method. The standard delta function is used wherever possible, and the modified delta function continuously transitions to the standard delta function away from the outer boundaries of the fluid domain. Three-dimensional computational results are presented to demonstrate the capabilities of our immersed boundary approach to simulating the fluid dynamics of heart valves.

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40

Bouaanani, Najib, Patrick Paultre, and Jean Proulx. "Dynamic response of a concrete dam impounding an ice-covered reservoir: Part II. Parametric and numerical study." Canadian Journal of Civil Engineering 31, no. 6 (December 1, 2004): 965–76. http://dx.doi.org/10.1139/l04-076.

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This paper presents a numerical and parametric study of the effect of an ice cover on the dynamic response of a concrete dam using the approach proposed in the companion paper in this issue. The method was programmed and implemented in a finite element code specialized for the seismic analysis of concrete dams. The 84-m-high Outardes 3 concrete gravity dam in northeastern Quebec was chosen as a model for this research. Some basic aspects of the numerical model are established in this paper and we show that the ice cover affects the dynamic response of the ice–dam–reservoir system. Main features of this influence are emphasized and discussed in a parametric study through the analysis of: (i) acceleration frequency response curves at the dam crest, (ii) hydrodynamic frequency response curves inside the reservoir, and (iii) the hydrodynamic pressure distribution on the upstream face of the dam. Key words: gravity dams, concrete dams, ice, reservoirs, mathematical models, ice–structure interaction, fluid–structure interaction, forced-vibration testing, finite elements modelling.

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41

Wang, Zhikai, Xiongliang Yao, Nana Yang, and Zhenhuan Xu. "Simulation of Fluid and Structure Interface with Immersed Boundary–Lattice Boltzmann Method Involving Turbulence Models." Mathematical Problems in Engineering 2018 (2018): 1–12. http://dx.doi.org/10.1155/2018/4072758.

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The multiple-relaxation-time (MRT) version of the immersed boundary–lattice Boltzmann (IB-LB) method is developed to simulate fluid-structure interfaces. The innovations include the implicit velocity correction to ensure no-slip boundary conditions and the incorporated Smagorinsky’s algebraic eddy viscosity for simulating turbulent flows. Both straight and curved interfaces are investigated. The streamlines penetration can be well prevented, which means the no-slip boundary condition can be guaranteed. Due to the existence of two coordinate systems: the Lagrangian coordinate system and the Eulerian coordinate system, the velocity and force properties on the structure can be easily calculated. Several benchmark simulation cases are carried out to verify the correctness of the model, including flow around circular cylinder at Re = 20, 150, and 3900 and flow around square cylinder at Re = 150 and 1000. The results agree well with previous studies, especially in the events of lower Reynolds numbers. Due to the three-dimensional turbulence vortex effects, the discrepancy increases are associated with higher Reynolds numbers. In addition, the effect of rotating velocity on the interaction process of the square cylinder in flows is researched, coupled with the capability of dealing with the moving boundaries.

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42

Wen, Guojun, Haojie Liu, Hongbo Huang, Yudan Wang, and Xinyu Shi. "Meshless method simulation and experimental investigation of crack propagation of CBM hydraulic fracturing." Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 73 (2018): 72. http://dx.doi.org/10.2516/ogst/2018074.

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For simulating CoalBed Methane (CBM) hydraulic fracturing using 3-D meshless method, this paper analyzed the hydraulic fracturing mechanism and cracking form for coal rock and established the geometric and mathematical models of hydraulic fracturing propagation in coal rock in terms of the Hillerborg model on crack opening displacement theory. With the theoretical basis of hydromechanics, the formulas for calculating hydraulic pressure inside the fracture by numerical simulation were deduced from the analysis on this fluid-structure interaction problem. The geometric and mathematical models established above were described by 3-D meshless Galerkin (EFG, Element-Free Galerkin) method and compiled into the numerical simulation program using VB and FORTRAN programming language to simulate the fracture propagation for an actual coal rock sample with a drilling hole as an example. Then the physical simulation experiment of hydraulic fracturing propagation of coal seam was conducted on the same coal rock sample. Through the direct observation with naked eyes and detection by advanced instruments of ESEM and Micro-CT, the shape and parameters of cracks on the surface of and inside the coal rock sample were achieved, which indicated that experimental results are reasonably consistent with numerical simulation results.

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43

Schwartz, Zvi. "Research: Game Theory: Mathematical Models Provide Insights into Hospitality Industry Phenomena." Journal of Hospitality & Tourism Research 21, no. 1 (February 1997): 48–70. http://dx.doi.org/10.1177/109634809702100106.

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Game theory is a mathematical modeling tool that considers the interaction among participants in economic activity. This article introduces some of the basic concepts of game theory, and demonstrates its applicability to hospitality industry research. The paper discusses essential elements of a game such as players, actions, strategies, payoffs and equilibria. The author explains how the information structure of a game determines its outcome, and examines the solution concepts of Nash Equilibrium in a simultaneous game. The Leader-Follower game and the concept of mixed strategies are also introduced. The study identifies topics currently discussed in the hospitality literature that are likely to benefit from this methodology. The discussion covers themes such as product differentiation and room rate policies, reputation and service quality, mergers and acquisitions and franchising.

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44

Grzesikiewicz, Wiesław, and Artur Zbiciak. "Mathematical Formulation of Soft-Contact Problems for Various Rheological Models of Damper." Shock and Vibration 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/8675016.

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The paper deals with analysis of selected soft-contact problems in discrete mechanical systems. Elastic-dissipative rheological schemes representing dampers as well as the notion of unilateral constraints were used in order to model interaction between colliding bodies. The mathematical descriptions of soft-contact problems involving variational inequalities are presented. The main finding of the paper is a method of description of soft-contact phenomenon between rigid object and deformable rheological structure by the system of explicit nonlinear differential-algebraic equations easy for numerical implementation. The results of simulations, that is, time histories of displacements and contact forces as well as hysteretic loops, are presented.

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45

Formaggia, Luca, Alexandra Moura, and Fabio Nobile. "On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations." ESAIM: Mathematical Modelling and Numerical Analysis 41, no. 4 (July 2007): 743–69. http://dx.doi.org/10.1051/m2an:2007039.

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46

Zhao, S. Z., X. Y. Xu, and M. W. Collins. "The numerical analysis of fluid-solid interactions for blood flow in arterial structures Part 1: A review of models for arterial wall behaviour." Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 212, no. 4 (April 1, 1998): 229–40. http://dx.doi.org/10.1243/0954411981534015.

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The structural response of a large artery is characteristically complex and includes the highly non-linear, history-dependent response of a nonhomogeneous anisotropic structure undergoing finite deformations. The mechanics of the arterial wall has been studied for nearly two centuries. The goals of such research range from the desire to have a basic knowledge and understanding of the mechanics and physiology of this complex structure to the need for data and methods for the design of arterial prostheses. In this paper, the models for arterial wall behaviour are critically reviewed. Firstly, the structure and general characteristics of the arterial wall are discussed. This is followed by a comprehensive review of the constitutive laws. Finally, structural analyses of the arterial wall by mathematical and numerical methods are discussed. Predictions using the authors' preferred models give focus to important issues, and in Part 2 the review and predictions are extended to the fluid-solid coupled situation.

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47

Shangguan, Wenbin. "NONLINEAR MODELING OF HYDRAULIC ENGINE MOUNTS OF A CAR POWERTRAIN WITH COMPUTATIONAL FLUID STRUCTURE INTERACTION FINITE ELEMENT ANALYSIS MODELS." Chinese Journal of Mechanical Engineering 40, no. 08 (2004): 80. http://dx.doi.org/10.3901/jme.2004.08.080.

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48

Mazinani, Iman, Mohammad Mohsen Sarafraz, Zubaidah Ismail, Ahmad Mustafa Hashim, Mohammad Reza Safaei, and Somchai Wongwises. "Fluid-structure interaction computational analysis and experiments of tsunami bore forces on coastal bridges." International Journal of Numerical Methods for Heat & Fluid Flow 31, no. 5 (March 22, 2021): 1373–95. http://dx.doi.org/10.1108/hff-02-2019-0127.

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Purpose Two disastrous Tsunamis, one on the west coast of Sumatra Island, Indonesia, in 2004 and another in North East Japan in 2011, had seriously destroyed a large number of bridges. Thus, experimental tests in a wave flume and a fluid structure interaction (FSI) analysis were constructed to gain insight into tsunami bore force on coastal bridges. Design/methodology/approach Various wave heights and shallow water were used in the experiments and computational process. A 1:40 scaled concrete bridge model was placed in mild beach profile similar to a 24 × 1.5 × 2 m wave flume for the experimental investigation. An Arbitrary Lagrange Euler formulation for the propagation of tsunami solitary and bore waves by an FSI package of LS-DYNA on high-performance computing system was used to evaluate the experimental results. Findings The excellent agreement between experiments and computational simulation is shown in results. The results showed that the fully coupled FSI models could capture the tsunami wave force accurately for all ranges of wave heights and shallow depths. The effects of the overturning moment, horizontal, uplift and impact forces on a pier and deck of the bridge were evaluated in this research. Originality/value Photos and videos captured during the Indian Ocean tsunami in 2004 and the 2011 Japan tsunami showed solitary tsunami waves breaking offshore, along with an extremely turbulent tsunami-induced bore propagating toward shore with significantly higher velocity. Consequently, the outcomes of this current experimental and numerical study are highly relevant to the evaluation of tsunami bore forces on the coastal, over sea or river bridges. These experiments assessed tsunami wave forces on deck pier showing the complete response of the coastal bridge over water.

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Buchori, L., Y. Bindar, D. Sasongko, and IGBN Makertihartha. "2-d mathematical and numerical modeling of fluid flow inside and outside packing in catalytic packed bed reactor." REAKTOR 5, no. 1 (June 13, 2017): 1. http://dx.doi.org/10.14710/reaktor.5.1.1-7.

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Generally, the momentum equation of fluid flow in porous media was solved by neglecting the terms of diffusion and convection such as Ergun, Darcy, Brinkman and Forchheimer models. Their model primarily applied for laminar flow. It is true that these model are limited to condition whether the models can be applied. Analytical solution for the model type above is available only for simple one-dimensional cases. For two or three-dimentional problem, numerical solution is the only solution. This work advances the flow model in porous media and provide two-dimentional flow field solution in porous media, which includes the diffusion and convection terms. The momentum lost due to flow and porous material interaction is modeled using the available Brinkman-Forchheimer equation. The numerical method to be used is finite volume method. This method is suitable for the characteristic of fluid flow in porous media which is averaged by a volume base. The effect of the solid and fluid interaction in porous media is the basic principle of the flow model in morous media. The Brinkman-Forchheimer consider the momentum lost term to be determined by a quadratic function of the velocity component. The momentum and the continuity equation are solved for two-dimentional cylindrical coordinat . the result were validated with the experimental data. The velocity of the porous media was treated to be radially oscillated. The result of velocity profile inside packing show a good agreement in their trend with the Stephenson and Steward experimental data. The local superficial velocity attains its global maximum and minimum at distances near 0.201 and 0.57 particle diameter, dp. velocity profile below packing was simulated. The result were validated with Schwartz and Smith experimental data. The result also show an excellent agreement with those experimental data.Keywords : finite volume method, porous media, flow distribution, velocity profile

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50

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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