Multiscale Simulation for the System of Radiation Hydrodynamics
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Multiscale Simulation for the System of Radiation Hydrodynamics Wenjun Sun1 · Song Jiang1 · Kun Xu2
· Guiyu Cao2
Received: 2 March 2020 / Revised: 8 August 2020 / Accepted: 8 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper aims at the simulation of multiple scale physics for the system of radiation hydrodynamics. The system couples the fluid dynamic equations with the radiative heat transfer. The coupled system is solved by the gas-kinetic scheme (GKS) for the compressible inviscid Euler flow and the unified gas-kinetic scheme (UGKS) for the non-equilibrium radiative transfer, together with the momentum and energy exchange between these two phases. For the radiative transfer, due to the possible large variation of fluid opacity in different regions, the transport of photons through the flow system is simulated by the multiscale UGKS, which is capable of naturally capturing the transport process from the photon’s free streaming to the diffusive wave propagation. Since both GKS and UGKS are finite volume methods, all unknowns are defined inside each control volume and are discretized consistently in the updates of hydrodynamic and radiative variables. For the coupled system, the scheme has the asymptotic preserving property, such as recovering the equilibrium diffusion limit for the radiation hydrodynamic system in the optically thick region, where the cell size is not limited by photon’s mean free path. A few test cases, such as radiative shock wave problems, are used to validate the current approach. Keywords Radiation hydrodynamics · Asymptotic preserving · Gas kinetic scheme · Unified gas kinetic scheme · Radiative shock wave
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Kun Xu [email protected] Wenjun Sun [email protected] Song Jiang [email protected] Guiyu Cao [email protected]
1
Institute of Applied Physics and Computational Mathematics, No. 2, FengHao East Road, HaiDian District, Beijing 100094, China
2
Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong 0123456789().: V,-vol
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Page 2 of 24
Journal of Scientific Computing
(2020) 85:25
1 Introduction This paper is about the construction of an asymptotic preserving numerical scheme for radiation hydrodynamics. Radiation hydrodynamics describes radiative transport through a fluid with coupled momentum and energy exchange. The system is routinely used in high energy density physics, astrophysics, the inertial confinement fusion (ICF), and other flows with very high temperature. For radiation hydrodynamics, radiation propagates through a moving hydrodynamic material. Due to the moving velocity of the material, the thermal radiative transfer equation includes relativistic material-motion correction whenever the radiation momentum deposition has a measurable impact on the material dynamics. The correction is applicable for flow with moving velocity being much smaller than the speed of light. Following the works of [1–3], we adopt Morel’s radiation hydrodynamic model in this
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