Self-consistent solution of cosmological radiation-hydrodynamics and chemical ionization

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.