A variational finite volume scheme for Wasserstein gradient flows
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DOI: 10.1007/s00211-020-01153-9
Abstract: We propose a variational finite volume scheme to approximate the solutions to Wasserstein gradient flows. The time discretization is based on an implicit linearization of the Wasserstein distance expressed thanks to Benamou-Brenier formula, whereas space… read more here.
Keywords: finite volume; gradient flows; scheme; wasserstein gradient ... See more keywords
Error estimate of the finite volume scheme for the Allen–Cahn equation
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DOI: 10.1007/s10543-017-0687-4
Abstract: The Allen–Cahn equation originates in the phase field formulation of phase transition phenomena. It is a reaction-diffusion ODE with a nonlinear reaction term which allows the formation of a diffuse phase interface. We first introduce… read more here.
Keywords: cahn equation; finite volume; scheme; allen cahn ... See more keywords
A Very High-Order Accurate Staggered Finite Volume Scheme for the Stationary Incompressible Navier–Stokes and Euler Equations on Unstructured Meshes
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DOI: 10.1007/s10915-016-0348-9
Abstract: We propose a sixth-order staggered finite volume scheme based on polynomial reconstructions to achieve high accurate numerical solutions for the incompressible Navier–Stokes and Euler equations. The scheme is equipped with a fixed-point algorithm with solution… read more here.
Keywords: order; finite volume; scheme; staggered finite ... See more keywords
Finite volume approximation of nonlinear agglomeration population balance equation on triangular grid
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DOI: 10.1016/j.jaerosci.2019.105430
Abstract: Abstract In this present work, a finite volume scheme for approximating a multidimensional nonlinear agglomeration population balance equation on a regular triangular grid is developed. The finite volume schemes developed in literature are restricted to… read more here.
Keywords: triangular grid; finite volume; volume; volume scheme ... See more keywords
Nonlinear Finite Volume Scheme Preserving Positivity for 2D Convection-Diffusion Equations on Polygonal Meshes
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DOI: 10.1155/2020/7343716
Abstract: In this paper, a nonlinear finite volume scheme preserving positivity for solving 2D steady convection-diffusion equation on arbitrary convex polygonal meshes is proposed. First, the nonlinear positivity-preserving finite volume scheme is developed. Then, in order… read more here.
Keywords: positivity; finite volume; scheme; volume scheme ... See more keywords