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Relevant bibliographies by topics / Finite volumes method

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Journal articles

Academic literature on the topic 'Finite volumes method'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 March 2023

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Journal articles on the topic "Finite volumes method"

1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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