A Unified Gas-Kinetic Particle Method for Frequency-Dependent Radiative Transfer Equations with Isotropic Scattering Process on Unstructured Mesh (Communications in Computational Physics, 2024)
In this paper, we extend the unified gas kinetic particle (UGKP) method tothe frequency-dependent radiative transfer equation with both absorption-emissionand scattering processes. The extended UGKP method could capture the diffusionand free transport limit and provide a smooth transition in the physical and frequencyspace in the regime between the above two limits. The proposed scheme has the properties of asymptotic-preserving and regime-adaptive, which make it an accurate andefficient scheme in the simulation of multiscale photon transport problems. In theUGKP formulation of flux construction and distribution closure, the coefficients of thenon-equilibrium free stream distribution and near-equilibrium Planck expansion areindependent of the time step. Therefore, even with a large CFL number, the UGKP canpreserve a physically consistent ratio of the non-equilibrium and the near-equilibriumproportion. The methodology of scheme construction is a coupled evolution of themacroscopic energy equation and the microscopic radiant intensity equation, wherethe numerical flux in the macroscopic energy equation and the closure in the microscopic radiant intensity equation are constructed based on the integral solution. Bothnumerical dissipation and computational complexity are well controlled, especially inthe optically thick regime. 2D multi-thread code on a general unstructured mesh hasbeen developed. Several numerical tests have been simulated to verify the numerical scheme and code, covering a wide range of flow regimes. The numerical schemeand code we developed are highly demanded and widely applicable in high-energyengineering applications.
Keywords: Frequency-dependent radiative transfer; multiscale method; asymptotic preserving; unified gas-kinetic particle method; unstructured mesh.