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Volume 27, Issue 4
A New Interpolation for Auxiliary Unknowns of the Monotone Finite Volume Scheme for 3D Diffusion Equations

Fei Zhao, Xiang Lai, Guangwei Yuan & Zhiqiang Sheng

DOI: 10.4208/cicp.OA-2019-0066

Commun. Comput. Phys., 27 (2020), pp. 1201-1233.

Published online: 2020-02

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  • 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.

  • Keywords

Diffusion equations, tetrahedral meshes, finite volume scheme, monotonicity, Anderson acceleration.

  • AMS Subject Headings

65M08, 65M12, 65B99

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zhaofei17@gscaep.ac.cn (Fei Zhao)

qxlai2000@sdu.edu.cn (Xiang Lai)

yuan_guangwei@iapcm.ac.cn (Guangwei Yuan)

sheng zhiqiang@iapcm.ac.cn (Zhiqiang Sheng)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-27-1201, author = {Zhao , FeiLai , XiangYuan , Guangwei and Sheng , Zhiqiang}, title = {A New Interpolation for Auxiliary Unknowns of the Monotone Finite Volume Scheme for 3D Diffusion Equations}, journal = {Communications in Computational Physics}, year = {2020}, volume = {27}, number = {4}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0066}, url = {http://global-sci.org/intro/article_detail/cicp/14848.html} }
TY - JOUR T1 - A New Interpolation for Auxiliary Unknowns of the Monotone Finite Volume Scheme for 3D Diffusion Equations AU - Zhao , Fei AU - Lai , Xiang AU - Yuan , Guangwei AU - Sheng , Zhiqiang JO - Communications in Computational Physics VL - 4 SP - 1201 EP - 1233 PY - 2020 DA - 2020/02 SN - 27 DO - http://doi.org/10.4208/cicp.OA-2019-0066 UR - https://global-sci.org/intro/article_detail/cicp/14848.html KW - Diffusion equations, tetrahedral meshes, finite volume scheme, monotonicity, Anderson acceleration. AB -

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.

Zhao , FeiLai , XiangYuan , Guangwei and Sheng , Zhiqiang. (2020). A New Interpolation for Auxiliary Unknowns of the Monotone Finite Volume Scheme for 3D Diffusion Equations. Communications in Computational Physics. 27 (4). 1201-1233. doi:10.4208/cicp.OA-2019-0066
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