A moving mesh finite difference method for equilibrium radiation diffusion equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:298

Article

Yang, Xiaobo¹  Huang, Weizhang²  Qiu, Jianxian^3,4 

[1] China Univ Min & Technol, Coll Sci, Dept Math, Xuzhou 221116, Jiangsu, Peoples R China

[2] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

[3] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China

[4] Xiamen Univ, Fujian Prov Key Lab Math Modeling & High Performa, Xiamen 361005, Fujian, Peoples R China

关键词: Moving mesh method;    Equilibrium radiation diffusion equations;    Prediction-correction;    Freezing coefficient;    Nonnegativity;    Cutoff;    Two-level mesh movement;   

DOI  :  10.1016/j.jcp.2015.06.014

来源: Elsevier

【 摘 要 】

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor-corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multimaterial, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free