A High-Order Finite Volume GENO Scheme with Implicit Time Integration for Three-Temperature Radiation Diffusion Equations

TL;DR

This paper introduces a high-order finite volume scheme with implicit time integration for three-temperature radiation diffusion equations, featuring a novel central GENO reconstruction for handling discontinuities and large gradients efficiently.

Contribution

The study develops a central GENO reconstruction for diffusion systems and a dual-time-stepping implicit method, enabling large time-step integration and improved accuracy for 3TRD equations.

Findings

Achieves high accuracy and robustness in numerical tests.

Effectively handles discontinuities and large temperature gradients.

Enables large time-step integration for complex diffusion systems.

Abstract

This study presents a high-order finite volume scheme capable of large time-step integration for three-temperature radiation diffusion (3TRD) equations, where conservation is naturally achieved through energy update. To handle local large gradients and discontinuities in temperature, a central generalized ENO (GENO) reconstruction is developed for diffusion systems, which achieves essentially non-oscillatory reconstruction for discontinuous solutions. Compared to conventional nonlinear reconstruction methods, its most distinctive feature is the central-type symmetric sub-stencils, which ensure consistency between the numerics and the isotropic nature of thermal diffusion. Additionally, the central GENO method provides smooth states of temperature and temperature gradient at interfaces, facilitating the evaluation of numerical fluxes. Furthermore, interface flux evaluation for cases with discontinuous physical property parameters is modeled. To address the extremely small time-step issue caused by stiff diffusion and source terms, a dual-time-stepping method based on implicit time discretization is developed for the first time in 3TRD systems, with the advantage of decoupling temporal discretization from complex nonlinear spatial discretization. A series of numerical examples validates the high accuracy, physical property preservation, strong robustness, and large time-step integration capability of the present high-order central GENO scheme.