A Lions Domain Decomposition Algorithm for Radiation Diffusion Equations on Non-matching Grids

Abstract

We develop a Lions domain decomposition algorithm based on a cell functional minimization scheme on non-matching multi-block grids for nonlinear radiation diffusion equations, which are described by the coupled radiation diffusion equations of electron, ion and photon temperatures. The L2 orthogonal projection is applied in the Robin transmission condition of non-matching surfaces. Numerical results show that the algorithm keeps the optimal accuracy on the whole computational domain, is robust enough on distorted meshes and curved surfaces, and the convergence rate does not depend on Robin coefficients. It is a practical and attractive algorithm in applying to the two-dimensional three-temperature energy equations of Z-pinch implosion simulation.

A Vertex-Centered and Positivity-Preserving Finite Volume Scheme for Two-Dimensional Three-Temperature Radiation Diffusion Equations on General Polygonal Meshes

“…Hence, solving 3-T radiation diffusion equations on distorted polygonal meshes is very interesting and important. In [45], a Lions domain decomposition algorithm based on a cell functional minimization scheme was studied on non-matching multi-block grids for nonlinear radiation diffusion equations. In [4], interface reconstruction was implemented within any cell that has more than one material and a new numerical scheme was developed for the 3-T radiation diffusion equations on polygonal or polyhedral meshes.…”