Multiscale solutions of radiative heat transfer by the discrete unified gas kinetic scheme

Abstract

The radiative transfer equation (RTE) has two asymptotic regimes characterized by the optical thickness, namely, optically thin and optically thick regimes. In the optically thin regime, a ballistic or kinetic transport is dominant. In the optically thick regime, energy transport is totally dominated by multiple collisions between photons; that is, the photons propagate by means of diffusion. To obtain convergent solutions to the RTE, conventional numerical schemes have a strong dependence on the number of spatial grids, which leads to a serious computational inefficiency in the regime where the diffusion is predominant. In this work, a discrete unified gas kinetic scheme (DUGKS) is developed to predict radiative heat transfer in participating media. Numerical performances of the DUGKS are compared in detail with conventional methods through three cases including one-dimensional transient radiative heat transfer, two-dimensional steady radiative heat transfer, and three-dimensional multiscale radiative heat transfer. Due to the asymptotic preserving property, the present method with relatively coarse grids gives accurate and reliable numerical solutions for large, small, and in-between values of optical thickness, and, especially in the optically thick regime, the DUGKS demonstrates a pronounced computational efficiency advantage over the conventional numerical models. In addition, the DUGKS has a promising potential in the study of multiscale radiative heat transfer inside the participating medium with a transition from optically thin to optically thick regimes.

Discrete unified gas kinetic scheme for multiscale anisotropic radiative heat transfer

“…Following Refs. [1,32], integrating Eq. (10) on a control volume V j centered at x j from time t n to t n+1 = t n + t, we can obtain…”

“…In the isotropic scattering condition ( ≡ 1), Eqs. (22) and (23) can be solved explicitly [1]. However, in anisotropic case, due to the complexity of the phase function ( (s , s)), Eqs.…”

“…Recently, an AP method, the unified gas kinetic scheme (UGKS) was successfully developed for radiative transfer problems [29][30][31]. Another asymptotic preserving multiscale method, the discrete unified gas kinetic scheme, which was initially designed for gas flows [32,33], was also extended to solve the radiative heat transfer problems in isotropic scattering media [1]. As the distribution function at a cell interface in DUGKS is constructed from the characteristic numerical solution rather than the local integral one in the UGKS, the DUGKS has a simpler structure and is more computational efficient.…”

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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.

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A Unified Gas-kinetic Scheme for Micro Flow Simulation Based on Linearized Kinetic Equation

“…The discrete unified gas-kinetic scheme (DUGKS) is developed by Guo el al. is also a multiscale scheme [5,19], and has been successfully applied in the field of micro flow [20,21], gas mixture [22], gas-particle multiphase flow [23], phonon transport [24], radiation [25], etc. The general synthetic iteration scheme was first proposed by Wu et al for the steady state solution of the linearized kinetic eqaution [6], and is recently extended to the simulation of nonlinear kinetic equation and diatomic gas [26,27].…”