A Nominally Second-Order Cell-Centered Finite Volume Scheme for Simulating Three-Dimensional Anisotropic Diffusion Equations on Unstructured Grids
作者机构：CEA/CESTA15 Avenue des Sablieres CS 6000133116 Le Barp cedexFrance. Institut fur MathematikUniversitat ZurichCH-8057 ZurichSwitzerland.
出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)
年 卷 期：2014年第16卷第9期
页 面：841-891页
核心收录：
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
基 金：EU ERC
主 题：Finite volume methods unstructured grids anisotropic diffusion parallel computing
摘 要：We present a finite volume based cell-centered method for solving diffusion equations on three-dimensional unstructured grids with general tensor *** main motivation concerns the numerical simulation of the coupling between fluid flows and heat *** corresponding numerical scheme is characterized by cell-centered unknowns and a local ***,the scheme results in a global sparse diffusion matrix,which couples only the cell-centered *** space discretization relies on the partition of polyhedral cells into sub-cells and on the partition of cell faces into *** is characterized by the introduction of sub-face normal fluxes and sub-face temperatures,which are auxiliary unknowns.A sub-cellbased variational formulation of the constitutive Fourier law allows to construct an explicit approximation of the sub-face normal heat fluxes in terms of the cell-centered temperature and the adjacent sub-face *** elimination of the sub-face temperatures with respect to the cell-centered temperatures is achieved locally at each node by solving a small and sparse linear *** system is obtained by enforcing the continuity condition of the normal heat flux across each sub-cell interface impinging at the node under *** parallel implementation of the numerical algorithm and its efficiency are described and *** accuracy and the robustness of the proposed finite volume method are assessed by means of various numerical test cases.
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