| 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). The equations exhibit strong nonlinearity, multi-scale characteristics, and sharp discontinuities, presenting considerable challenges for high-order numerical solutions. To address these, we develop a two-dimensional high-order conservative arbitrary Lagrangian-Eulerian (ALE) scheme. We first design a high-order explicit Lagrangian scheme under the equilibrium diffusion limit based on multi-resolution weighted essentially non-oscillatory (WENO) reconstruction for spatial discretization, strong stability-preserving Runge-Kutta time discretization, and HLLC numerical fluxes, with a focus on discussing the positivity-preserving property of the high-order scheme. In the meantime, to overcome the severe time step restrictions of explicit schemes, we propose a high-order Explicit-Implicit-Null (EIN) Lagrangian scheme by adding linear artificial diffusion terms to the equations, treating nonlinear terms explicitly and handling linear diffusion terms implicitly. Finally, to address the challenges posed by mesh distortion and deformation in Lagrangian methods, we incorporate mesh rezoning and remapping algorithms to develop a high-order conservative ALE scheme suitable for handling complicated RHE. Additionally, we extended the high-order conservative ALE scheme to the non-equilibrium three-temperature RHE. Numerical experiments demonstrate that these schemes are high-order accurate, conservative, non-oscillatory, and can capture the interfaces automatically. |
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