Self-Consistent Solution of Cosmological Radiation-Hydrodynamics and Chemical Ionization

TL;DR

This paper presents a fully-implicit, scalable numerical method for solving complex coupled PDE systems involving radiation, hydrodynamics, and chemical ionization in cosmology, demonstrating accuracy and robustness on large problems.

Contribution

It introduces a novel implicit Newton-based approach with multigrid preconditioning for coupled radiation-hydrodynamics-chemistry equations in cosmology.

Findings

Method is accurate and robust on test problems.

Scalable to very large problem sizes.

Effective use of multigrid-preconditioned solvers.

Abstract

We consider a PDE system comprising compressible hydrodynamics, flux-limited diffusion radiation transport and chemical ionization kinetics in a cosmologically-expanding universe. Under an operator-split framework, the cosmological hydrodynamics equations are solved through the Piecewise Parabolic Method, as implemented in the Enzo community hydrodynamics code. The remainder of the model, including radiation transport, chemical ionization kinetics, and gas energy feedback, form a stiff coupled PDE system, which we solve using a fully-implicit inexact Newton approach, and which forms the crux of this paper. The inner linear Newton systems are solved using a Schur complement formulation, and employ a multigrid-preconditioned conjugate gradient solver for the inner Schur systems. We describe this approach and provide results on a suite of test problems, demonstrating its accuracy, robustness, and scalability to very large problems.