Flux balanced approximation with least-squares gradient for diffusion equation on polyhedral mesh
type: Item
instance of: scholarly article
title: Flux balanced approximation with least-squares gradient for diffusion equation on polyhedral mesh
zbMATH Open document ID: 1465.65116
author: Peter Frolkovič
author: Karol Mikula
author: Jooyoung Hahn
author: Dirk Martin
author: B. Basara
published in: Discrete and Continuous Dynamical Systems. Series S
publication date: 2021-05-07T00:00:00Z
review text: The authors present a finite volume method for the diffusion equations that can be applied to general polyhedral meshes. It is based on the flux balanced approximation using the least-squares gradient with the distance weighted harmonic mean of piecewise continuous diffusion coefficient. The degrees of freedom are the values at the centers of the cells. The flux balanced approximation is proposed without numerically computing the gradient itself at the faces of computational cells in order to find a normal diffusive flux. It is shown that in the case of discontinuous diffusion coefficient, it is suitable to use the restricted least-squares gradient that respects the discontinuity in the approximation. The method can be used in the iterative way, where each iteration uses a matrix in the 1-ring neighborhood. Several numerical examples are presented to illustrate some advantages of the proposed method.
reviewed by: Abdallah Bradji
Mathematics Subject Classification ID: 65N08
Mathematics Subject Classification ID: 65M08
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65Y10
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 94A08
Mathematics Subject Classification ID: 35Q94
zbMATH DE Number: 7345415
zbMATH Keywords: diffusion equations
zbMATH Keywords: finite volume methods
zbMATH Keywords: polyhedral mesh
zbMATH Keywords: least-squares gradient
zbMATH Keywords: deferred correction
zbMATH Keywords: cross diffusion
describes a project that uses: FlowLab
describes a project that uses: OpenFOAM
describes a project that uses: AVL
MaRDI profile type: Publication
full work available at URL: dcdss.2020350
OpenAlex ID: W3026016847
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DOI: 10.3934/DCDSS.2020350
description: scientific article; zbMATH DE number 7345415