Dynamic Implicit 3D Adaptive Mesh Refinement for Non-Equilibrium Radiation Diffusion

TL;DR

This paper introduces a comprehensive computational framework combining implicit time integration, adaptive mesh refinement, and advanced solvers to efficiently simulate non-equilibrium radiation diffusion in complex, multi-scale systems.

Contribution

It presents a novel integration of implicit methods, dynamic 3D AMR, and multilevel preconditioning tailored for nonlinear multiphysics radiation diffusion problems.

Findings

Efficient long-term simulation of stiff radiation diffusion equations.

Reduced computational costs through dynamic mesh refinement.

Achieved level-independent convergence with multilevel preconditioners.

Abstract

The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial confinement fusion. The associated initial boundary value problems that are encountered often exhibit a wide range of scales in space and time and are extremely challenging to solve. To efficiently and accurately simulate these systems we describe our research on combining techniques that will also find use more broadly for long term time integration of nonlinear multiphysics systems: implicit time integration for efficient long term time integration of stiff multiphysics systems, local control theory based step size control to minimize the required global number of time steps while controlling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton-Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent solver convergence.