Journal articles: 'Finite volumes method'

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Calgaro, Caterina, Claire Colin, and Emmanuel Creusé. "A combined finite volumes ‐ finite elements method for a low‐Mach model." International Journal for Numerical Methods in Fluids 90, no. 1 (2019): 1–21. http://dx.doi.org/10.1002/fld.4706.

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HUANG, ZHECONG, HONG ZHENG, and FENG DAI. "MESHLESS FINITE VOLUME METHOD WITH SMOOTHING." International Journal of Computational Methods 11, no. 06 (2014): 1350087. http://dx.doi.org/10.1142/s0219876213500874.

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Starting from the integral forms of the equilibrium condition and the constitutive law over the small volumes centered at the nodes, this study approximates stresses and displacements independently by means of the meshless approximation. By interpreting the meshless approximation from a new perspective, the procedure does not need to differentiate the nodal shape functions. The stresses can be approximated as accurately as the displacements, even if the shape functions for the stresses and the displacements are both taken as those simple interpolation functions such as the Shepard functions. Besides, in general no background mesh is needed. Illustrated by some elastic–plastic problems, the procedure enjoys high efficiency and excellent numerical properties.

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Droniou, Jérôme, Robert Eymard, Thierry Gallouët, and Raphaèle Herbin. "The Gradient Discretisation Method for Linear Advection Problems." Computational Methods in Applied Mathematics 20, no. 3 (2020): 437–58. http://dx.doi.org/10.1515/cmam-2019-0060.

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AbstractWe adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence analysis of various numerical schemes, corresponding to the methods known to be GDMs, such as finite elements (conforming or non-conforming, standard or mass-lumped), finite volumes on rectangular or simplicial grids, and other recent methods developed for general polytopal meshes. The scheme is of centred type, with added linear or non-linear numerical diffusion. We complement the convergence analysis with numerical tests based on the mass-lumped {\mathbb{P}_{1}} conforming and non-conforming finite element and on the hybrid finite volume method.

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Bowers, Abigail, Jared Bunn, and Myles Kim. "Efficient Methods to Calculate Partial Sphere Surface Areas for a Higher Resolution Finite Volume Method for Diffusion-Reaction Systems in Biological Modeling." Mathematical and Computational Applications 25, no. 1 (2019): 2. http://dx.doi.org/10.3390/mca25010002.

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Computational models for multicellular biological systems, in both in vitro and in vivo environments, require solving systems of differential equations to incorporate molecular transport and their reactions such as release, uptake, or decay. Examples can be found from drugs, growth nutrients, and signaling factors. The systems of differential equations frequently fall into the category of the diffusion-reaction system due to the nature of the spatial and temporal change. Due to the complexity of equations and complexity of the modeled systems, an analytical solution for the systems of the differential equations is not possible. Therefore, numerical calculation schemes are required and have been used for multicellular biological systems such as bacterial population dynamics or cancer cell dynamics. Finite volume methods in conjunction with agent-based models have been popular choices to simulate such reaction-diffusion systems. In such implementations, the reaction occurs within each finite volume and finite volumes interact with one another following the law of diffusion. The characteristic of the reaction can be determined by the agents in the finite volume. In the case of cancer cell growth dynamics, it is observed that cell behavior can be different by a matter of a few cell size distances because of the chemical gradient. Therefore, in the modeling of such systems, the spatial resolution must be comparable to the cell size. Such spatial resolution poses an extra challenge in the development and execution of the computational model due to the agents sitting over multiple finite volumes. In this article, a few computational methods for cell surface-based reaction for the finite volume method will be introduced and tested for their performance in terms of accuracy and computation speed.

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Khattri, Sanjay Kumar. "Nonlinear elliptic problems with the method of finite volumes." Differential Equations and Nonlinear Mechanics 2006 (2006): 1–16. http://dx.doi.org/10.1155/denm/2006/31797.

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We present a finite volume discretization of the nonlinear elliptic problems. The discretization results in a nonlinear algebraic system of equations. A Newton-Krylov algorithm is also presented for solving the system of nonlinear algebraic equations. Numerically solving nonlinear partial differential equations consists of discretizing the nonlinear partial differential equation and then solving the formed nonlinear system of equations. We demonstrate the convergence of the discretization scheme and also the convergence of the Newton solver through a variety of practical numerical examples.

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LIU, S. J., H. WANG, and H. ZHANG. "SMOOTHED FINITE ELEMENTS LARGE DEFORMATION ANALYSIS." International Journal of Computational Methods 07, no. 03 (2010): 513–24. http://dx.doi.org/10.1142/s0219876210002246.

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The smoothed finite element method (SFEM) was developed in order to eliminate certain shortcomings of the finite element method (FEM). SFEM enjoys some of the flexibilities of meshfree methods. One advantage of SFEM is its applicability to modeling large deformations. Due to the absence of volume integration and parametric mapping, issues such as negative volumes and singular Jacobi matrix do not occur. However, despite these advantages, SFEM has never been applied to problems with extreme large deformation. For the first time, we apply SFEM to extreme large deformations. For two numerical problems, we demonstrate the advantages of SFEM over FEM. We also show that SFEM can compete with the flexibility of meshfree methods.

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Rusanov, P. G. "Algorithmic concepts of method of solid bodies." Izvestiya MGTU MAMI 7, no. 3-1 (2013): 124–36. http://dx.doi.org/10.17816/2074-0530-68053.

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Method of solid bodies is included in the group of adaptive numerical methods of continuum mechanics. It is applicable for the analysis of motion of solids, liquids and gases. Using construction techniques this method provides a priori division of the generalized coordinates for the finite object of the research volume into fast and slow variables. The total number of slow variables does not exceed 6 N, where N is a number of finite volumes. The paper mentions methods of forming mathematical model of the object state relatively to the slow variables without the participation of the fast variables.

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Gaitonde, A. L., and S. P. Fiddes. "A three-dimensional moving mesh method for the calculation of unsteady transonic flows." Aeronautical Journal 99, no. 984 (1995): 150–60. http://dx.doi.org/10.1017/s0001924000027135.

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AbstractA three-dimensional moving mesh method for solving the Euler equations describing the compressible flow about a wing undergoing arbitrary motions and deformations is described. A finite-volume formulation is chosen where the volumes distort as the wing moves or deforms. By using transfinite interpolation, a technique for generating the required sequence of grids has been developed. Furthermore, as the speeds of the grid at the vertices of the finite volumes are required by the flow solver, transfinite interpolation is also used to obtain these by interpolation of the boundary speeds. A two-dimensional version of the method has also been developed and results for both two- and three-dimensional transonic flows are presented and compared with experimental data where available.

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Molina-Aiz, F. D., D. L. Valera, H. Fatnassi, T. Boulard, and J. C. Roy. "NUMERICAL SIMULATION OF NATURAL VENTILATION IN GREENHOUSES: A COMPARISON BETWEEN FINITE VOLUMES METHOD AND FINITE ELEMENTS METHOD." Acta Horticulturae, no. 801 (November 2008): 971–78. http://dx.doi.org/10.17660/actahortic.2008.801.115.

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Gaitonde, A. L., and S. P. Fiddes. "A Comparison of a Cell-Centre Method and a Cell-Vertex Method for the Solution of the Two-Dimensional Unsteady Euler Equations on a Moving Grid." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 209, no. 3 (1995): 203–13. http://dx.doi.org/10.1243/pime_proc_1995_209_291_02.

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A moving-mesh system for the solution of two-dimensional Euler equations describing the compressible flow about an aerofoil undergoing arbitrary motions and deformations is presented. A finite volume formulation is chosen, where the volumes distort as the aerofoil moves. Independent motion of the inner and outer boundaries is permitted. By using transfinite interpolation, a fast technique for generating the required sequence of grids has been developed. Furthermore, as the flow speeds of the grid at the vertices of the finite volumes are required by any flow solver, these are also obtained by transfinite interpolation of the boundary speeds. The moving mesh has been implemented using two flow solvers, one is a cell-centre method and the other is a cell-vertex method. The flow solvers have been used to calculate a series of test cases and have produced good results in terms of detailed pressure distributions and load loops.

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Santos, R. S., D. P. A. Peña, D. D. S. Diniz, G. A. Costa, J. G. A. Queiroz, and S. R. F. Neto. "Brick Drying Simulations by Finite Volume Method." Materials Science Forum 930 (September 2018): 115–19. http://dx.doi.org/10.4028/www.scientific.net/msf.930.115.

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There are numerous studies on the application of ceramic materials, such as bricks, in the various engineering and manufacturing fields. Ceramic bricks are manufactured from humidified clay and are classified as structural ceramics. When exposed to drying the process is not precisely controlled, defects such as cracks, deformations and warping can arise, which compromise the final physical and structural properties of the product. Seeking to solve the procedure through simulations, this work presents a numerical study on a brick drying. A three-dimensional transient model is presented to predict the temperature of the holed ceramic brick and the distribution of the humidity content in a drying situation inside a temperature controlled oven, the heat transfer and mass phenomena are present. As simulations were done in the ANSYS CFX® program, which uses the Finite Volumes Method and presented satisfactory results when compared with the experimental works.

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Jo, Gwanghyun, and Do Y. Kwak. "Immersed finite element methods for convection diffusion equations." AIMS Mathematics 8, no. 4 (2023): 8034–59. http://dx.doi.org/10.3934/math.2023407.

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<abstract><p>In this work, we develop two IFEMs for convection-diffusion equations with interfaces. We first define bilinear forms by adding judiciously defined convection-related line integrals. By establishing Gårding's inequality, we prove the optimal error estimates both in $ L^2 $ and $ H^1 $-norms. The second method is devoted to the convection-dominated case, where test functions are piecewise constant functions on vertex-associated control volumes. We accompany the so-called upwinding concepts to make the control-volume based IFEM robust to the magnitude of convection terms. The $ H^1 $ optimal error estimate is proven for control-volume based IFEM. We document numerical experiments which confirm the analysis.</p></abstract>

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Ambrus, Jaime, C. R. Maliska, F. S. V. Hurtado, and A. F. C. da Silva. "Finite Volume Methods with Multi-Point Flux Approximation with Unstructured Grids for Diffusion Problems." Defect and Diffusion Forum 297-301 (April 2010): 670–75. http://dx.doi.org/10.4028/www.scientific.net/ddf.297-301.670.

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This paper addresses the key issue of calculating fluxes at the control-volume interfaces when finite-volumes are employed for the solution of partial differential equations. This calculation becomes even more significant when unstructured grids are used, since the flux approximation involving only two grid points is no longer correct. Two finite volume methods with the ability in dealing with unstructured grids, the EbFVM-Element-based Finite Volume Method and the MPFA-Multi-Point Flux Approximation are presented, pointing out the way the fluxes are numerically evaluated. The methods are applied to a porous media flow with full permeability tensors and non-orthogonal grids and the results are compared with analytical solutions. The results can be extended to any diffusion operator, like heat and mass diffusion, in anisotropic media.

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Betancourt Schwarz, Manuel, Mohamed Tahar Mabrouk, Carlos Santo Silva, Pierrick Haurant, and Bruno Lacarrière. "Modified finite volumes method for the simulation of dynamic district heating networks." Energy 182 (September 2019): 954–64. http://dx.doi.org/10.1016/j.energy.2019.06.038.

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Rachid, F. B. Freitas, J. H. Carneiro de Araujo, and R. M. Baptista. "Predicting Mixing Volumes in Serial Transport in Pipelines." Journal of Fluids Engineering 124, no. 2 (2002): 528–34. http://dx.doi.org/10.1115/1.1459078.

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This paper presents a model for predicting the contaminated mixing volume arising in pipeline batch transfers without physical separators. The proposed technique represents an improvement over the existing methods since it takes into account time-dependent flow rates and accurate concentration-varying axial dispersion coefficients. The governing equation of the model forms a nonlinear boundary-value problem that is solved by a finite element method coupled to the Newton’s method. A comparison among the theoretical predictions of this method, a field test, and other classical procedures show that the proposed method exhibits the best estimate over the whole range of admissible concentrations investigated.

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Dostál, Jiří, and Vladimír Havlena. "Mixed Mesh Finite Volume Method for 1D Hyperbolic Systems with Application to Plug-Flow Heat Exchangers." Mathematics 9, no. 20 (2021): 2609. http://dx.doi.org/10.3390/math9202609.

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We present a finite volume method formulated on a mixed Eulerian-Lagrangian mesh for highly advective 1D hyperbolic systems altogether with its application to plug-flow heat exchanger modeling/simulation. Advection of sharp moving fronts is an important problem in fluid dynamics, and even a simple transport equation cannot be solved precisely by having a finite number of nodes/elements/volumes. Finite volume methods are known to introduce numerical diffusion, and there exist a wide variety of schemes to minimize its occurrence; the most recent being adaptive grid methods such as moving mesh methods or adaptive mesh refinement methods. We present a solution method for a class of hyperbolic systems with one nonzero time-dependent characteristic velocity. This property allows us to rigorously define a finite volume method on a grid that is continuously moving by the characteristic velocity (Lagrangian grid) along a static Eulerian grid. The advective flux of the flowing field is, by this approach, removed from cell-to-cell interactions, and the ability to advect sharp fronts is therefore enhanced. The price to pay is a fixed velocity-dependent time sampling and a time delay in the solution. For these reasons, the method is best suited for systems with a dominating advection component. We illustrate the method’s properties on an illustrative advection-decay equation example and a 1D plug flow heat exchanger. Such heat exchanger model can then serve as a convection-accurate dynamic model in estimation and control algorithms for which it was developed.

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Silva, J. B. C., S. S. Mansur, and R. C. Lima. "LARGE EDDY SIMULATION OF TURBULENT INCOMPRESSIBLE FLUID FLOWS BY A NINE-NODES CONTROL VOLUME-FINITE ELEMENT METHOD." Revista de Engenharia Térmica 4, no. 2 (2005): 173. http://dx.doi.org/10.5380/reterm.v4i2.5412.

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The main purpose of this work is the numerical computation of turbulent incompressible fluid flows by a nine-node control volume finite element method (CVFEM) using the methodology of large-eddy simulation.. The domain is discretized using nine nodes finite elements and the equations are integrated into control volumes around the nodes of the finite elements. The Navier?Stokes equations are filtered for simulation of the large scales variables and the sub-grid scales stress appearing due to the filtering process are modeled through the eddy viscosity model of Smagorinsky. The two-dimensional benchmark problem of the lid-driven cavity flow is solved to validate the numerical code and preliminary results for the horizontal and vertical velocity profiles at the centerlines of the cavity and the stream functions are presented and compared with available results from the literature.

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Deuring, Paul, and Robert Eymard. "L2-stability of a finite element – finite volume discretization of convection-diffusion-reaction equations with nonhomogeneous mixed boundary conditions." ESAIM: Mathematical Modelling and Numerical Analysis 51, no. 3 (2017): 919–47. http://dx.doi.org/10.1051/m2an/2016042.

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We consider a time-dependent and a steady linear convection-diffusion-reaction equation whose coefficients are nonconstant. Boundary conditions are mixed (Dirichlet and Robin−Neumann) and nonhomogeneous. Both the unsteady and the steady problem are approximately solved by a combined finite element – finite volume method: the diffusion term is discretized by Crouzeix−Raviart piecewise linear finite elements on a triangular grid, and the convection term by upwind barycentric finite volumes. In the unsteady case, the implicit Euler method is used as time discretization. This scheme is shown to be unconditionally L2-stable, uniformly with respect to diffusion, except if the Robin−Neumann boundary condition is inhomogeneous and the convective velocity is tangential at some points of the Robin−Neumann boundary. In that case, a negative power of the diffusion coefficient arises. As is shown by a counterexample, this exception cannot be avoided.

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Droniou, Jérome, Neela Nataraj, and Devika Shylaja. "Numerical Analysis for the Pure Neumann Control Problem Using the Gradient Discretisation Method." Computational Methods in Applied Mathematics 18, no. 4 (2018): 609–37. http://dx.doi.org/10.1515/cmam-2017-0054.

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AbstractThe article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that directly applies to a wide range of numerical schemes, from conforming and non-conforming finite elements, to mixed finite elements, to finite volumes and mimetic finite differences methods. Optimal order error estimates for state, adjoint and control variables for low-order schemes are derived under standard regularity assumptions. A novel projection relation between the optimal control and the adjoint variable allows the proof of a super-convergence result for post-processed control. Numerical experiments performed using a modified active set strategy algorithm for conforming, non-conforming and mimetic finite difference methods confirm the theoretical rates of convergence.

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Abd, Abdul Salam, and Ahmad S. Abushaikha. "On the Performance of the Node Control Volume Finite Element Method for Modeling Multi-phase Fluid Flow in Heterogeneous Porous Media." Transport in Porous Media 135, no. 2 (2020): 409–29. http://dx.doi.org/10.1007/s11242-020-01481-2.

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Abstract In this paper, we critique the performance of the node control volume finite element (NCVFE) method for modeling multi-phase fluid flow in heterogeneous media. The NCVFE method solves for the pressure at the vertices of elements and a control volume mesh is constructed around them. Material properties are defined on elements, while transport is simulated on the control volumes. These two meshes are not aligned producing inaccurate results and artificial fluid smearing when modeling multi-phase fluid flow in heterogeneous media. We perform numerical tests to quantify and visualize the extent of this artificial fluid smearing in domains with different material properties. The domains are composed of tetrahedron finite elements. Large artificial fluid smearing is observed in coarse meshes; however, it decreases with the increase in mesh resolution. These findings prompt the use of high-resolution meshes for the method and the need for development of novel numerical methods to address this unphysical flow.

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Ganaoui, El, and El Alami. "A lattice Boltzmann coupled to finite volumes method for solving phase change problems." Thermal Science 13, no. 2 (2009): 205–16. http://dx.doi.org/10.2298/tsci0902205e.

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Madzvamuse, Anotida, and Andy H. W. Chung. "The bulk-surface finite element method for reaction–diffusion systems on stationary volumes." Finite Elements in Analysis and Design 108 (January 2016): 9–21. http://dx.doi.org/10.1016/j.finel.2015.09.002.

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Peng, Szu-Hsien. "1D and 2D Numerical Modeling for Solving Dam-Break Flow Problems Using Finite Volume Method." Journal of Applied Mathematics 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/489269.

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The purpose of this study is to model the flow movement in an idealized dam-break configuration. One-dimensional and two-dimensional motion of a shallow flow over a rigid inclined bed is considered. The resulting shallow water equations are solved by finite volumes using the Roe and HLL schemes. At first, the one-dimensional model is considered in the development process. With conservative finite volume method, splitting is applied to manage the combination of hyperbolic term and source term of the shallow water equation and then to promote 1D to 2D. The simulations are validated by the comparison with flume experiments. Unsteady dam-break flow movement is found to be reasonably well captured by the model. The proposed concept could be further developed to the numerical calculation of non-Newtonian fluid or multilayers fluid flow.

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Sacharczuk, Jacek, and Dawid Taler. "Theoretical modeling and experimental study of auxiliary concrete accumulator for solar heating systems." MATEC Web of Conferences 240 (2018): 02009. http://dx.doi.org/10.1051/matecconf/201824002009.

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This article presents the issue of the use of the control-volume finite-elements method (CVFEM) to solve transient heat conduction problem in the ceramic or concrete structure of heat storage system. The system can be used as auxiliary storage in solar based domestic hot water (DHW) and heating installations. The storage system consists of modular symmetric components forming parallel air channels. The modular design and symmetry of cross section enables to build a simple numerical model using a coarse mesh of finite volumes. It allows solving the problem using the simple algorithm. Analyzed method of modeling provides a short computation time while maintaining high calculation accuracy.

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Piltyay, S. I., А. V. Bulashenko, O. V. Bykovskyi, and O. V. Bulashenko. "ESTIMATION OF FEM AND FDTD METHODS FOR SIMULATION OF ELECTROMAGNETIC CHARACTERISTICS OF POLARIZATION TRANSFORMING DEVICES WITH DIAPHRAGMS." Radio Electronics, Computer Science, Control, no. 4 (January 10, 2022): 34–48. http://dx.doi.org/10.15588/1607-3274-2021-4-4.

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Context. Today, there is a rapid expansion of the range of modern branches of science and technology, which actively use satellite telecommunication systems to receive, process and transmit various information. These radioelectronic systems quite often require an increase of the volumes of information, which they are processing and transmitting. Increase of the volumes of transmitted information in two times can be achieved by using dual-polarization antenna systems and devices. Nowadays, most part of the specialists, who are engaged in the development of various modern polarization-processing microwave devices, carry out their numerical modeling and optimization using variational techniques, methods of integral equations, method of fields matching in partial regions. The methods with division of the internal region of the device into elementary cells are applied most actively. Among them in the time domain the most often used approach is finite difference method with the decomposition at hexagonal mesh, while and in the frequency domain the finite elements method with the adaptive tetrahedral mesh is applied. Therefore, the estimation of the speed and accuracy of these methods with the purpose of determination of more effective among them is a relevant problem. Objective. The goal of the research is comparison of speed and accuracy of the calculations of electromagnetic characteristics of waveguide polarizers using FEM and FDTD methods, as well as the comparison of the convergence of these methods for the analysis of polarization-processing microwave devices with diaphragms. Method. For the calculations and analysis of electromagnetic characteristics in the article we used the method of finite differences in the time domain (FDTD) and the method of finite elements in the frequency domain (FEM). In FEM the volume is split into the tetrahedral mesh cells. In FDTD the computational domain is divided into hexagonal mesh cells. Results. It was found that the convergence of voltage standing wave ratio for the waveguide polarizer is fast for both methods. It was obtained that the convergence of the characteristics of differential phase shift, axial ratio, and crosspolar discrimination of the developed microwave device turned out to be much more sensitive to the number of mesh cells used. Moreover, in the research it was obtained by calculations that the computation time by the finite elements method in the frequency domain is more than 2 times less than the corresponding time required for calculations by the finite difference time domain method. When using the finite elements method in the frequency domain the corresponding number of tetrahedral mesh cells is 10 times less than the number of hexagonal mesh cells, which are used in the finite difference time domain method. Conclusions. Performed investigations have shown that FEM in the frequency domain, which applies an adaptive tetrahedral mesh, is more efficient than the FDTD method for the calculations of phase and polarization characteristics of modern waveguide polarizers and other microwave devices for various applications.

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Graff, Joseph S., Roger L. Davis, and John P. Clark. "Computational structural dynamics general solution procedure using finite volumes." Journal of Algorithms & Computational Technology 16 (January 2022): 174830262210840. http://dx.doi.org/10.1177/17483026221084030.

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A method for the solution of the three-dimensional structural dynamics equations with large strains using a finite volume technique is presented. The proposed solution procedure is second order accurate in space and employs a second-order accurate dual time-stepping scheme. The momentum conservation equations are written in terms of the Piola-Kirchhoff stresses. The stress tensor is related to the Lagrangian strain tensor through the St. Venant-Kirchhoff constitutive relationship. The structural solver presented is verified through two test cases. The first test case is a three-dimensional cantilever beam subject to a gravitational load that is verified using theory and two-dimensional simulations reported in literature. The second test case is a three-dimensional highly deformable cantilever plate subject to a gravitational load. The results of this case are verified through a comparison with the modal response calculated by commercially available software. The focus of the current effort is the development and verification of the structural dynamics portion of a future fully coupled monolithic fluid-thermal-structure interaction code package.

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Xu, Lei, Wu Zhang, Zhengzheng Yan, Zheng Du, and Rongliang Chen. "A novel median dual finite volume lattice Boltzmann method for incompressible flows on unstructured grids." International Journal of Modern Physics C 31, no. 12 (2020): 2050173. http://dx.doi.org/10.1142/s0129183120501739.

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A novel median dual finite volume lattice Boltzmann method (FV-LBM) for the accurate simulation of incompressible flows on unstructured grids is presented in this paper. The finite volume method is adopted to discretize the discrete velocity Boltzmann equation (DVBE) on median dual control volumes (CVs). In the previous studies on median dual FV-LBMs, the fluxes for each partial face have to be computed separately. In the present second-order scheme, we assume the particle distribution functions (PDFs) to be constant for all faces grouped around a particular edge. The fluxes are then evaluated using the low-diffusion Roe scheme at the midpoint of the edge, and the PDFs at the faces of the CV are obtained through piecewise linear reconstruction of the left and right states. The gradients of the PDFs are computed with the Green–Gauss approach. The presented scheme is validated on four benchmark flows: (a) pressure driven Poiseuille flow; (b) the backward-facing step flow with [Formula: see text], 100, 200 and 300; (c) the lid-driven flow with [Formula: see text] and 1000; and (d) the steady viscous flow past a circular cylinder with [Formula: see text], 20 and 40.

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Ondami, Bienvenu. "THE METHOD OF LINES WITH A FINITE VOLUMES APPROACH FOR TRANSIENT CONVECTION-DIFFUSION PROBLEMS." Journal of Mathematical Sciences: Advances and Applications 44 (April 10, 2017): 91–109. http://dx.doi.org/10.18642/jmsaa_7100121779.

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Ho, Mark, Guan Yeoh, John Reizes, and Victoria Timchenko. "The intersection marker method for 3D interface tracking of deformable surfaces in finite volumes." International Journal for Numerical Methods in Fluids 81, no. 4 (2015): 220–44. http://dx.doi.org/10.1002/fld.4182.

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Kudimova, Anna, and Andrey Nasedkin. "Analysis of porosity influence on the effective moduli of ceramic matrix PZT composite using the simplified finite element model." Journal of Advanced Dielectrics 09, no. 06 (2019): 1950043. http://dx.doi.org/10.1142/s2010135x19500437.

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The problem of determining the effective moduli of a ceramic matrix piezocomposite with respect to multiscale porosity was considered. To solve the homogenization problem, the method of effective moduli in the standard formulation, the finite element method and the ANSYS computational package were used. Various models of two-phase and three-phase composites consisting of a piezoceramic matrix, elastic inclusions of corundum and pores of various sizes have been investigated. Finite element models of representative volumes of 3–0 and 3–0–0 connectivities were developed. The results of computational experiments showed that effective moduli depend quite significantly not only on the volume fractions of inclusions and pores, but also on the structure and size of pores in comparison with the characteristic sizes of inclusions.

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Bugajev, Andrej, Gerda Jankevičiūtė, and Natalija Tumanova. "The Mathematical Modelling of Heat Transfer in Electrical Cables." Electrical, Control and Communication Engineering 5, no. 1 (2014): 46–53. http://dx.doi.org/10.2478/ecce-2014-0007.

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Abstract This paper describes a mathematical modelling approach for heat transfer calculations in underground high voltage and middle voltage electrical power cables. First of the all typical layout of the cable in the sand or soil is described. Then numerical algorithms are targeted to the two-dimensional mathematical models of transient heat transfer. Finite Volume Method is suggested for calculations. Different strategies of nonorthogonality error elimination are considered. Acute triangles meshes were applied in two-dimensional domain to eliminate this error. Adaptive mesh is also tried. For calculations OpenFOAM open source software which uses Finite Volume Method is applied. To generate acute triangles meshes aCute library is used. The efficiency of the proposed approach is analyzed. The results show that the second order of convergence or close to that is achieved (in terms of sizes of finite volumes). Also it is shown that standard strategy, used by OpenFOAM is less efficient than the proposed approach. Finally it is concluded that for solving real problem a spatial adaptive mesh is essential and adaptive time steps also may be needed.

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MASSÉ, NADIA, CHRISTIAN PRAX, and EMMANUEL REDON. "A FLUX-BASED CONSERVATION APPROACH FOR ACOUSTIC PROBLEMS." Journal of Computational Acoustics 16, no. 01 (2008): 31–53. http://dx.doi.org/10.1142/s0218396x08003440.

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In this paper a Control Volume Finite Element Method for harmonic acoustic problems is presented. A dispersion analysis for control volume constructed on Q1 finite elements is compared to Galerkin FEM. The spatial convergence is also given in an eigenfrequency determination process for a cavity. The application for exterior acoustic problems is also studied by dividing the whole field into inner and outer domains using a fictitious boundary. A control volume formulation is used to compute the inner field of the truncated problem, and several approaches are combined to describe the outer field behavior on the outside of the fictitious boundary. The task of coupling is easily implemented through the balance of local flux through polygonal volumes. A two-dimensional configuration with a circular interface demonstrates the validity of this approach.

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Mathur, S. R., and J. Y. Murthy. "Radiative Heat Transfer in Periodic Geometries Using a Finite Volume Scheme." Journal of Heat Transfer 121, no. 2 (1999): 357–64. http://dx.doi.org/10.1115/1.2825988.

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A procedure for computing radiative heat transfer in translationally and rotationally periodic geometries is presented. The finite volume scheme is applied to meshes composed of arbitrary polyhedral control volumes. The angular domain is discretized into a finite number of control angles over which radiant energy is conserved. At periodic boundaries, control angle overhang occurs because of the misalignment of the arbitrary periodic face with the global angular discretization and due to the arbitrary rotation of adjacent modules with respect to each other. A discretization scheme using control angle pixelation is developed to conservatively transfer radiant energy between adjacent modules. The method is tested for a variety of radiation problems and shown to perform satisfactorily.

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Steinbrecher, Ivo, Matthias Mayr, Maximilian J. Grill, Johannes Kremheller, Christoph Meier, and Alexander Popp. "A mortar-type finite element approach for embedding 1D beams into 3D solid volumes." Computational Mechanics 66, no. 6 (2020): 1377–98. http://dx.doi.org/10.1007/s00466-020-01907-0.

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AbstractIn this work we present a novel computational method for embedding arbitrary curved one-dimensional (1D) fibers into three-dimensional (3D) solid volumes, as e.g. in fiber-reinforced materials. The fibers are explicitly modeled with highly efficient 1D geometrically exact beam finite elements, based on various types of geometrically nonlinear beam theories. The surrounding solid volume is modeled with 3D continuum (solid) elements. An embedded mortar-type approach is employed to enforce the kinematic coupling constraints between the beam elements and solid elements on non-matching meshes. This allows for very flexible mesh generation and simple material modeling procedures in the solid, since it can be discretized without having to account for the reinforcements, while still being able to capture complex nonlinear effects due to the embedded fibers. Several numerical examples demonstrate the consistency, robustness and accuracy of the proposed method, as well as its applicability to rather complex fiber-reinforced structures of practical relevance.

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Muñoz-Rojas, Pablo A., and M. Vaz. "Flux Evaluation in Anisotropic Heat Conduction Using the Modified Local Green’s Function Method (MLGFM): Comparative Studies." Materials Science Forum 553 (August 2007): 100–105. http://dx.doi.org/10.4028/www.scientific.net/msf.553.100.

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The Modified Local Green’s Function Method (MLGFM) is an integral method which uses appropriately chosen Green’s function projections obtained numerically with the aid of auxiliary finite element problems. Its applicability includes those cases for which a fundamental solution does not exist or is very cumbersome. The MLGFM was studied intensely in the 90´s with promising results, especially for tractions and heat fluxes at the boundaries. The present contribution compares this method for heat flux evaluation in anisotropic media with finite volumes and finite elements. The latter approximates heat fluxes using a superconvergent patch recovery scheme, whereas the former computes flux quantities directly at nodes. The numerical example uses linear elements and includes non-homogeneous temperature and flux boundary conditions.

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Arghir, Mihai, and Jean Fre^ne. "A Triangle Based Finite Volume Method for the Integration of Lubrication’s Incompressible Bulk Flow Equations." Journal of Tribology 123, no. 1 (2000): 118–24. http://dx.doi.org/10.1115/1.1326444.

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It is well known that for a reduced Reynolds number Re*=ρVH/μs˙H/L greater than unity, inertia forces have a dominant effect in the transport equations, thus rendering the classical lubrication equation inapplicable. The so called “bulk flow” system of equations is then the appropriate mathematical model for describing the flow in bearing and seals operating at Re*⩾1. The difficulty in integrating this system of equations is that one has to deal with coupled pressure and velocity fields. Analytic methods have a very narrow application range so a numerical method has been proposed by Launder and Leschziner in 1978. It represents a natural extrapolation of the successful SIMPLE algorithm applied to the bulk flow system of equations. The algorithm used rectangular, staggered control volumes and represented the state of the art at that moment. In the present work we introduced a method using triangular control volumes. The basic advantage of triangles versus rectangles is that non rectangular domains can be dealt without any a priori limitation. The present paper is focused on the description of the discretized equations and of the solution algorithm. Validations for bearings and seals operating in incompressible, laminar and turbulent flow regime are finally proving the accuracy of the method.

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Kim, Dongha, Jinho Woo, and Won-Bae Na. "Intensively Stacked Placement Models of Artificial Reef Sets Characterized by Wake and Upwelling Regions." Marine Technology Society Journal 51, no. 3 (2017): 60–70. http://dx.doi.org/10.4031/mtsj.51.3.7.

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AbstractThe wake and upwelling regions of artificial reefs (ARs), and sets, groups, and complexes thereof, are critical factors in engineering AR design and estimating fishing grounds, which are often facilitated by ARs. This study proposes six AR set placement models, constructed based on previous field observations, to characterize their wake and upwelling regions quantitatively through an element-based finite-volume method. These AR sets are hexahedral (Hexa), rectangular (Rect), pyramidal (Pyra), trigonal (Tri), tetragonal (Tetra), and pentagonal (Pent) sets, and their usable volumes are all fixed at 800 m3 (the minimum requirement of South Korean AR provision) in the flow analysis models. The analyses showed that Rect and Hexa provide the largest wake volumes of 496 and 352 m3, respectively, while Rect and Tetra provide the largest upwelling volumes of 13,106 and 6,116 m3, respectively. Finally, the maximum reductions in the wake and upwelling regions due to uniform settlement of 20%, which is equivalent to a usable volume loss of 160 m3, were 67% and 35%, respectively. Thus, wake regions are more sensitive to usable volume loss than upwelling regions.

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Brankovic, Milan, and Mark E. Everett. "A Method for Modeling Acoustic Waves in Moving Subdomains." Acoustics 4, no. 2 (2022): 394–405. http://dx.doi.org/10.3390/acoustics4020024.

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Forward modeling plays a key role in both the creation of predictive models and the study of the surrounding environment through inversion methods. Due to their competitive computational cost and modest algorithmic complexity, finite difference methods (FDM) are commonly used to model the acoustic wave equation. An algorithm has been developed to decrease the computational cost of acoustic-wave forward modeling that can be applied to most finite difference methods. An important feature of the algorithm is the calculation, at each time step, of the pressure in only a moving subdomain which contains the grid points across which waves are passing. The computation is skipped at grid points at which the waves are negligibly small or non-existent. The novelty in this work comes from flexibility of the subdomain and its ability to closely follow the developing wavefield. To demonstrate the efficacy of the algorithm, it is applied to a standard finite difference scheme and validated against 2-D modeling results. The algorithm herein can play an important role in the reduction in computation time of seismic data analysis as the volumes of seismic data increase due to developments in data acquisition technology.

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Chan, Yiu Pong, Chak Yin Tang, Brian W. Darvell, and Chi Pong Tsui. "Effect of Filler Shape and Volume Fraction on Strain Damage of Particulate-Reinforced Dental Composites." Materials Science Forum 532-533 (December 2006): 117–20. http://dx.doi.org/10.4028/www.scientific.net/msf.532-533.117.

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The effect of filler shape and volume fraction on the micromechanical damage behavior of particulate-reinforced dental composites was investigated using the finite element method. Threedimensional unit cell models for various filler volumes and shapes, using hydroxyapatite in Bis- GMA as a model system, were used. Young’s modulus and stress concentration factor were calculated. The effects of filler shape on the ease of initiation of strain damage in the matrix and onset of particle-matrix debonding are discussed.

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Alakashi, Abobaker Mohammed, and Bambang Basuno. "Comparison between Cell-Centered Schemes Computer Code and Fluent Software for a Transonic Flow Pass through an Array of Turbine Stator Blades." Applied Mechanics and Materials 437 (October 2013): 271–74. http://dx.doi.org/10.4028/www.scientific.net/amm.437.271.

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The Finite Volume Method (FVM) is a discretization method which is well suited for the numerical simulation of various types (elliptic, parabolic or hyperbolic, for instance) of conservation laws; it has been extensively used in several engineering fields. The Finite volume method uses a volume integral formulation of the problem with a finite partitioning set of volumes to discretize the equations [. the developed computer code based Cell-centered scheme and Fluent software had been used to investigate the inviscid Transonic Flow Pass Through an array of Turbine Stator Blades. The governing equation of fluid motion of the flow problem in hand is assumed governed by the compressible Euler Equation. Basically this equation behave as a mixed type of partial differential equation elliptic and hyperbolic type of partial differential equation. If the local Mach number is less than one, the governing equation will behave as elliptic type of differential equation while if the Mach number is greater than one it will behave as hyperbolic type of differential equation. To eliminate the presence a mixed type behavior, the governing equation of fluid motion are treated as the governing equation of unsteady flow although the problem in hand is steady flow problems. Presenting the Euler equation in their unsteady form makes the equation becomes hyperbolic with respect to time. There are various Finite Volume Methods can used for solving hyperbolic type of equation, such as Cell-centered scheme [, Roe Upwind Scheme [ and TVD Scheme [. The present work use a cell centered scheme applied to the case of flow pass through an array of turbine stator blades. The comparison carried out with the result provided by Fluent Software for three different value of back pressure. The developed computer code shows the result close to the Fluent software although the Fluent software use a Time Averaged Navier stokes equation as its governing equation of fluid motion.

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Caldas Steinstraesser, Joao G., Vincent Guinot, and Antoine Rousseau. "Modified parareal method for solving the two-dimensional nonlinear shallow water equations using finite volumes." SMAI journal of computational mathematics 7 (January 14, 2022): 159–84. http://dx.doi.org/10.5802/smai-jcm.75.

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Botts, Jonathan M., and Ning Xiang. "An application of the finite difference time‐domain method to the study of coupled volumes." Journal of the Acoustical Society of America 125, no. 4 (2009): 2735. http://dx.doi.org/10.1121/1.4784523.

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Helluy, Philippe, and Frédéric Golay. "Applications of the finite volumes method for complex flows: From the theory to the practice." Flow, Turbulence and Combustion 76, no. 4 (2006): 315–29. http://dx.doi.org/10.1007/s10494-006-9020-z.

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Nigro, Nicholas J., Benjamin P. Zellmer, Dongkai Shangguan, and Ping S. Lee. "A modified finite element method for determining equilibrium capillary surfaces of liquids with specified volumes." International Journal for Numerical Methods in Fluids 33, no. 6 (2000): 833–46. http://dx.doi.org/10.1002/1097-0363(20000730)33:6<833::aid-fld33>3.0.co;2-1.

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Kyei, Yaw. "Higher-Order Accurate Finite Volume Discretization of the Three-Dimensional Poisson Equation Based on An Equation Error Method." International Journal for Innovation Education and Research 6, no. 6 (2018): 107–23. http://dx.doi.org/10.31686/ijier.vol6.iss6.1076.

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Efficient higher-order accurate finite volume schemes are developed for the threedimensional Poisson’s equation based on optimizations of an equation error expansion on local control volumes. A weighted quadrature of local compact fluxes and the flux integral form of the equation are utilized to formulate the local equation error expansions. Efficient quadrature weights for the schemes are then determined through a minimization of the error expansion for higher-order accurate discretizations of the equation. Consequently, the leading numerical viscosity coefficients are more accurately and completely determined to optimize the weight parameters for uniform higher-order convergence suitable for effective numerical modeling of physical phenomena. Effectiveness of the schemes are evaluated through the solution of the associated eigenvalue problem. Numerical results and analysis of the schemes demonstrate the effectiveness of the methodology.

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Qi, Jin, Yue Wang, and Jiequan Li. "Remapping-Free Adaptive GRP Method for Multi-Fluid Flows I: One Dimensional Euler Equations." Communications in Computational Physics 15, no. 4 (2014): 1029–44. http://dx.doi.org/10.4208/cicp.140313.111013s.

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AbstractIn this paper, a remapping-free adaptive GRP method for one dimensional (1-D) compressible flows is developed. Based on the framework of finite volume method, the 1-D Euler equations are discretized on moving volumes and the resulting numerical fluxes are computed directly by the GRP method. Thus the remapping process in the earlier adaptive GRP algorithm [17,18] is omitted. By adopting a flexible moving mesh strategy, this method could be applied for multi-fluid problems. The interface of two fluids will be kept at the node of computational grids and the GRP solver is extended at the material interfaces of multi-fluid flows accordingly. Some typical numerical tests show competitive performances of the new method, especially for contact discontinuities of one fluid cases and the material interface tracking of multi-fluid cases.

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Kalis, H. "EFFECTIVE FINITE-DIFFERENCE METHODS FOR THE SOLUTIONS OF FILTRATION PROBLEMS IN MULTILAYER DOMAINS." Mathematical Modelling and Analysis 2, no. 1 (1997): 84–91. http://dx.doi.org/10.3846/13926292.1997.9637071.

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In papers [1,2] there were consider different assumptions for averaging methods along the vertical coordinate.These methods were applied for the mathematical simulation of the mass transfer process in multilayered underground systems. A specific feature of these problems is that it is necessity to solve the 3‐D initial‐boundary‐value problems for parabolic type partial differential equations of second order with piece‐wise parameters in multilayer domain.Therefore here an effective finite‐difference method for solving a problem of the above type is developed.This method may be considered as a generalization of the method of finite volumes [3] for the layered systems. In the case of constant piece‐wise coefficients we obtain the exact discrete approximation of steady‐state 1‐D boundary‐value problem.This procedure allows to reduce the 3-D problem to a system of 2-D problems and the 2-D problem to a system of 1-D problems.

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Chen, Hongquan, Tsubasa Onishi, Jaeyoung Park, and Akhil Datta-Gupta. "Computing Pressure Front Propagation Using the Diffusive-Time-of-Flight in Structured and Unstructured Grid Systems via the Fast-Marching Method." SPE Journal 26, no. 03 (2021): 1366–86. http://dx.doi.org/10.2118/201771-pa.

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Summary Diffusive-time-of-flight (DTOF), representing the travel time of pressure front propagation, has found many applications in unconventional reservoir performance analysis. The computation of DTOF typically involves upwind finite difference of the Eikonal equation and solution using the fast-marching method (FMM). However, the application of the finite difference-based FMM to irregular grid systems remains a challenge. In this paper, we present a novel and robust method for solving the Eikonal equation using finite volume discretization and the FMM. The implementation is first validated with analytical solutions using isotropic and anisotropic models with homogeneous reservoir properties. Consistent DTOF distributions are obtained between the proposed approach and the analytical solutions. Next, the implementation is applied to unconventional reservoirs with hydraulic and natural fractures. Our approach relies on cell volumes and connections (transmissibilities) rather than the grid geometry, and thus can be easily applied to complex grid systems. For illustrative purposes, we present applications of the proposed method to embedded discrete fracture models (EDFMs), dual-porosity dual-permeability models (DPDK), and unstructured perpendicular-bisectional (PEBI) grids with heterogeneous reservoir properties. Visualization of the DTOF provides flow diagnostics, such as evolution of the drainage volume of the wells and well interactions. The novelty of the proposed approach is its broad applicability to arbitrary grid systems and ease of implementation in commercial reservoir simulators. This makes the approach well-suited for field applications with complex grid geometry and complex well architecture.

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ČUNDERLÍK, Róbert, Matej MEDĽA, and Karol MIKULA. "Local quasigeoid modelling in Slovakia using the finite volume method on the discretized Earth's topography." Contributions to Geophysics and Geodesy 50, no. 3 (2020): 287–302. http://dx.doi.org/10.31577/congeo.2020.50.3.1.

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The paper presents local quasigeoid modelling in Slovakia using the finite volume method (FVM). FVM is used to solve numerically the fixed gravimetric boundary value problem (FGBVP) on a 3D unstructured mesh created above the real Earth's surface. Terrestrial gravimetric measurements as input data represent the oblique derivative boundary conditions on the Earth's topography. To handle such oblique derivative problem, its tangential components are considered as surface advection terms regularized by a surface diffusion. The FVM numerical solution is fixed to the GOCE-based satellite-only geopotential model on the upper boundary at the altitude of 230 km. The horizontal resolution of the 3D computational domain is 0.002 × 0.002 deg and its discretization in the radial direction is changing with altitude. The created unstructured 3D mesh of finite volumes consists of 454,577,577 unknowns. The FVM numerical solution of FGBVP on such a detailed mesh leads to large-scale parallel computations requiring 245 GB of internal memory. It results in the disturbing potential obtained in the whole 3D computational domain. Its values on the discretized Earth's surface are transformed into the local quasigeoid model that is tested at 404 GNSS/levelling benchmarks. The standard deviation of residuals is 2.8 cm and decreases to 2.6 cm after removing 9 identified outliers. It indicates high accuracy of the obtained FVM-based local quasigeoid model in Slovakia.

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Nawroth, T. "Interpretation of small angle scattering data by molecular models according to the “Finite Volumes Method” (FVM)." Physica B: Condensed Matter 156-157 (January 1989): 493–95. http://dx.doi.org/10.1016/0921-4526(89)90712-6.

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Journal articles on the topic 'Finite volumes method'

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