A multigroup diffusion solver using pseudo transient continuation for a radiation-hydrodynamic code with patch-based AMR

TL;DR

This paper introduces a robust, parallel multigroup radiation diffusion solver with adaptive mesh refinement, employing pseudo transient continuation to ensure stability and convergence in complex radiation-hydrodynamic simulations.

Contribution

It develops a novel multilevel implicit solver with pseudo transient continuation for radiation diffusion in AMR frameworks, enhancing robustness and accuracy.

Findings

The solver achieves stable convergence in complex simulations.

It effectively handles multigroup radiation diffusion with adaptive mesh refinement.

Results demonstrate improved robustness and computational efficiency.

Abstract

We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiation-hydrodynamic code with adaptive mesh refinement (AMR). The patch-based AMR algorithm refines in both space and time creating a hierarchy of levels, coarsest to finest. The physics modules are time-advanced using operator splitting. On each level, separate level-solve packages advance the modules. Our multigroup level-solve adapts an implicit procedure which leads to a two-step iterative scheme that alternates between elliptic solves for each group with intra-cell group coupling. For robustness, we introduce pseudo transient continuation (PTC). We analyze the magnitude of the PTC parameter to ensure positivity of the resulting linear system, diagonal dominance and convergence of the two-step scheme. For AMR, a level defines a subdomain for refinement. For diffusive processes such as MGD, the refined level uses Dirichet boundary data at the coarse-fine interface and the data is derived from the coarse level solution. After advancing on the fine level, an additional procedure, the sync-solve (SS), is required in order to enforce conservation. The MGD SS reduces to an elliptic solve on a combined grid for a system of G equations, where G is the number of groups. We adapt the partial temperature scheme for the SS; hence, we reuse the infrastructure developed for scalar equations. Results are presented. (Abridged)