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 - <p style="text-align: justify;">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.</p>