A unified gas-kinetic particle method for frequency-dependent radiative transfer equations with isotropic scattering process on unstructured mesh

TL;DR

This paper introduces an extended unified kinetic particle method for frequency-dependent radiative transfer equations, capable of accurately modeling multiscale photon transport with properties like asymptotic-preserving and regime-adaptive features.

Contribution

The paper develops a novel extended UGKP scheme that seamlessly transitions between diffusion and free transport regimes in frequency-dependent radiative transfer, with efficient implementation on unstructured meshes.

Findings

The scheme accurately captures multiscale photon transport phenomena.

Numerical tests verify the scheme's effectiveness across different regimes.

The method reduces numerical dissipation and computational complexity.

Abstract

In this paper, we extend the unified kinetic particle (UGKP) method to the frequency-dependent radiative transfer equation with both absorption-emission and scattering processes. The extended UGKP method could not only capture the diffusion and free transport limit, but also provide a smooth transition in the physical and frequency space in the regime between the above two limits. The proposed scheme has the properties of asymptotic-preserving, regime-adaptive, and entropy-preserving, which make it an accurate and efficient scheme in the simulation of multiscale photon transport problems. The methodology of scheme construction is a coupled evolution of macroscopic energy equation and the microscopic radiant intensity equation, where the numerical flux in macroscopic energy equation and the closure in microscopic radiant intensity equation are constructed based on the integral solution. Both numerical dissipation and computational complexity are well controlled especially in the optical thick regime. A 2D multi-thread code on a general unstructured mesh has been developed. Several numerical tests have been simulated to verify the numerical scheme and code, covering a wide range of flow regimes. The numerical scheme and code that we developed are highly demanded and widely applicable in the high energy density engineering applications.