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

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.

Figure 1

Spatial and temporal distributions of radiation energy due to continuous collimated radiation: (a) incident radiation and (b) radiative flux.

Figure 2

Time history of transmittance due to square pulse irradiation with a width of $\beta c{t}_{\mathrm{p}}=1$: (a) $\beta =1$ and (b) $\beta =10$.

Figure 3

Time history of transmittance due to Gauss pulse irradiation with a width of $\beta c{t}_{\mathrm{p}}=0.5$: (a) $\beta =10,\omega =0.5$; (b) $\beta =20,\omega =0.5$; (c)  $\beta =20,\omega =0.9$; and (d) $\beta =20,\omega =0.9$.

Figure 4

Nondimensional net radiative heat flux at the hot wall for the radiative equilibrium problem: (a) DUGKS solutions at different optical thickness, (b) FVM solutions at different optical thickness, and (c) the effects of wall emissivity.

Figure 5

Nondimensional net wall radiative heat flux at the radiative nonequilibrium: (a) effects of scattering albedo and (b) effects of extinction coefficient.

Figure 6

Radiative intensity distributions in the square enclosure with different optical thicknesses: (a) Galerkin FEM solutions, (b) analytical solutions, and (c) DUGKS solutions.

Figure 7

Schematic of the cubic enclosure subjected to an incident short-pulse laser.

Figure 8

The predicted transient transmittance signals for various parameters: (a) ${\beta }_{\max }=20,\omega =0.5$; (b) ${\beta }_{\max }=20,\omega =0.95$; (c) ${\beta }_{\max }=50,\omega =0.5$; and (d) ${\beta }_{\max }=50,\omega =0.95$.