Reproducing Kernel Particle Method for Radiative Heat Transfer in 1D Participating Media

Abstract

The reproducing kernel particle method (RKPM), which is a Lagrangian meshless method, is employed for the calculation of radiative heat transfer in participating media. In the present method, for each discrete particle (i.e., spatial node) within a local support domain, the approximate formulas of the radiative intensity and its derivatives are constructed by the reproducing kernel interpolation function, and the residual function is obtained when these parameters are substituted into the radiative transfer equation. Then the least-squares point collocation technique (LSPCT) is introduced by minimizing the summation of residual function. Five test cases are considered and quantified to verify the meshless method, including isotropic scattering medium, first-order forward scattering medium, pure absorbing medium, absorbing scattering medium, and absorbing, scattering emitting medium. The results are in good agreement with the benchmark methods, showing the reproducing kernel particle method is an efficient, accurate, and stable method for the calculation of radiative transfer in participating media.

Extending the diffusion approximation to the boundary using an integrated diffusion model

“…The discrepancy between them is clearly seen near the boundaries, implying the nonlinear property of the incident energy flow distribution. 13 The results demonstrate that IDM can capture both the noncontinuity and nonlinearity of the solution from the linearized BTE, which is more desirable compared to the diffusion approximation in the large K n scenarios. In Figure 2 when solving Eq.…”

“…(3) without further assumptions. 13 It is worth mentioning that the solution of the linearized BTE G B t is used to check the accuracy of IDM. Note that Θ(0) and Θ(τ L ), as well as Ψ, are only functions of τ L .…”