TY - JOUR
T1 - An Efficient Positivity-Preserving Finite Volume Scheme for the Nonequilibrium Three-Temperature Radiation Diffusion Equations on Polygonal Meshes
AU - Su , Shuai
AU - Tang , Huazhong
AU - Wu , Jiming
JO - Communications in Computational Physics
VL - 2
SP - 448
EP - 485
PY - 2021
DA - 2021/05
SN - 30
DO - http://doi.org/10.4208/cicp.OA-2020-0088
UR - https://global-sci.org/intro/article_detail/cicp/19121.html
KW - Radiation diffusion equations, positivity-preserving, high efficiency, stability, finite
volume method.
AB - <p style="text-align: justify;">This paper develops an efficient positivity-preserving finite volume scheme
for the two-dimensional nonequilibrium three-temperature radiation diffusion equations on general polygonal meshes. The scheme is formed as a predictor-corrector algorithm. The corrector phase obtains the cell-centered solutions on the primary mesh,
while the predictor phase determines the cell-vertex solutions on the dual mesh independently. Moreover, the flux on the primary edge is approximated with a fixed
stencil and the nonnegative cell-vertex solutions are not reconstructed. Theoretically,
our scheme does not require any nonlinear iteration for the linear problems, and can
call the fast nonlinear solver (e.g. Newton method) for the nonlinear problems. The
positivity, existence and uniqueness of the cell-centered solutions obtained on the corrector phase are analyzed, and the scheme on quasi-uniform meshes is proved to be $L^2$- and $H^1$-stable under some assumptions. Numerical experiments demonstrate the
accuracy, efficiency and positivity of the scheme on various distorted meshes.</p>