Discrete unified gas kinetic scheme for multiscale anisotropic radiative heat transfer

Xinliang Song,Zhaoli Guo,Chuang Zhang,Xiafeng Zhou

doi:10.1186/s42774-019-0026-3

Abstract

In this work, a discrete unified gas kinetic scheme (DUGKS) is developed for radiative transfer in anisotropic scattering media. The method is an extension of a previous one for isotropic radiation problems [1]. The present scheme is a finite-volume discretization of the anisotropic gray radiation equation, where the anisotropic scattering phase function is approximated by the Legendre polynomial expansion. With the coupling of free transport and scattering processes in the reconstruction of the flux at cell interfaces, the present DUGKS has the nice unified preserving properties such that the cell size is not limited by the photon mean free path even in the optical thick regime. Several one- and two-dimensional numerical tests are conducted to validate the performance of the present DUGKS, and the numerical results demonstrate that the scheme is a reliable method for anisotropic radiative heat transfer problems.

Highlights

1 Introduction Radiative heat transfer appears in many engineering applications, such as short-pulsed laser in turbid media [2], radiative base heating from rocket exhaust plums [3], radiation in liquid rocket engines [4], nonequilibrium radiative hypersonic flows [5], and some other processes [6–9]
An AP method, the unified gas kinetic scheme (UGKS) was successfully developed for radiative transfer problems [29–31]. Another asymptotic preserving multiscale method, the discrete unified gas kinetic scheme, which was initially designed for gas flows [32, 33], was extended to solve the radiative heat transfer problems in isotropic scattering media [1]
5 Summary In present work, we developed a discrete unified gas kinetic scheme for radiative transfer with anisotropic scattering media based on the radiative transfer equation

Summary

Introduction

Radiative heat transfer appears in many engineering applications, such as short-pulsed laser in turbid media [2], radiative base heating from rocket exhaust plums [3], radiation in liquid rocket engines [4], nonequilibrium radiative hypersonic flows [5], and some other processes [6–9]. An AP method, the unified gas kinetic scheme (UGKS) was successfully developed for radiative transfer problems [29–31] Another asymptotic preserving multiscale method, the discrete unified gas kinetic scheme, which was initially designed for gas flows [32, 33], was extended to solve the radiative heat transfer problems in isotropic scattering media [1]. Where σ is the Stefan-Boltzmann constant and T is the local temperature of the medium, and (s , s) is the scattering phase function, which describes the fraction of the radiative energy scattered into the outgoing direction s from the incoming direction s , and is the corresponding solid angle domain. Unlike the isotropic scattering problems where the scattering phase function is constant ( ≡ 1), the scattering phase function in anisotropic scattering problems changes according to the scattering angle In this study it is approximated by a finite series of Legendre polynomials [17, 35, 36], i.e., N (s , s) = (cosψ) = Cj(α1, α2)Pj(cosψ),.

Numerical scheme

Boundary conditions

Radiation in a slab with different wall temperatures