High order conservative Lagrangian schemes for two-dimensional radiation hydrodynamics equations in the equilibrium-diffusion limit

Abstract

Radiation hydrodynamics equations (RHE) refer to the study of how interactions between radiation and matter influence thermodynamic states and dynamic flow, which has been widely applied to high temperature hydrodynamics, such as inertial confinement fusion (ICF) and astrophysical gaseous stars. Solving RHE accurately and robustly even under the equilibrium diffusion approximation is a challenging task. To address this, we develop two types of high order conservative Lagrangian schemes for RHE in the equilibrium-diffusion limit for the two dimensional case on the Lagrangian moving mesh. Based on the multi-resolution WENO reconstruction for the spatial discretization and strong stability preserving Runge-Kutta (SSP-RK) time discretization, we first develop an explicit Lagrangian scheme with the HLLC numerical flux to achieve high order accuracy in space and time. We also discuss the positivity-preserving property of the high order explicit Lagrangian scheme. To overcome the severe time step restriction arising from the nonlinear radiation diffusion term in the explicit scheme, we further present a high order explicit-implicit-null (EIN) Lagrangian scheme. By adding a sufficiently large linear diffusion term on both sides of the scheme, we treat the complicated nonlinear parts explicitly and efficiently, and treat the added linear diffusion term on the right-hand side implicitly with a relaxed time step restriction. According to our numerical experiments, these two types of Lagrangian schemes are high order accurate, conservative and can capture the interfaces automatically. Additionally, the explicit scheme is found to be non-oscillatory and can preserve positivity while maintaining the original high order accuracy.