A New Interpolation for Auxiliary Unknowns of the Monotone Finite Volume Scheme for 3D Diffusion Equations
Year: 2020
Author: Fei Zhao, Xiang Lai, Guangwei Yuan, Zhiqiang Sheng
Communications in Computational Physics, Vol. 27 (2020), Iss. 4 : pp. 1201–1233
Abstract
A monotone cell-centered finite volume scheme for diffusion equations on tetrahedral meshes is established in this paper, which deals with tensor diffusion coefficients and strong discontinuous diffusion coefficients. The first novelty here is to propose a new method of interpolating vertex unknowns (auxiliary unknowns) with cell-centered unknowns (primary unknowns), in which a sufficient condition is given to guarantee the non-negativity of vertex unknowns. The second novelty of this paper is to devise a modified Anderson acceleration, which is based on an iterative combination of vertex unknowns and will be denoted as AA-Vertex algorithm, in order to solve the nonlinear scheme efficiently. Numerical testes indicate that our new method can obtain almost second order accuracy and is more accurate than some existing methods. Furthermore, with the same accuracy, the modified Anderson acceleration is much more efficient than the usual one.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2019-0066
Communications in Computational Physics, Vol. 27 (2020), Iss. 4 : pp. 1201–1233
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 33
Keywords: Diffusion equations tetrahedral meshes finite volume scheme monotonicity Anderson acceleration.
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