Multilevel quasidiffusion method with mixed-order time discretization for multigroup thermal radiative transfer problems

摘要

In this paper we present a numerical method for solving multigroup thermal radiative transfer (TRT) problems in 2D Cartesian geometry. It is based on the Quasidiffusion (aka Variable Eddington Factor) method and defined by the multilevel system of multigroup high-order radiative transfer (RT) equations and multigroup and grey low-order equations for moments of the intensity with the exact closures. We apply time integration schemes of different orders of accuracy to approximate the high-order and low-order equations. The first-order scheme is used for the high-order RT equations. The second-order scheme is applied to the low-order equations. This improves the accuracy of the TRT solution while using robust and relatively inexpensive scheme for the high-order RT equations. The solution of the low-order equations is non-monotonic because the hyperbolic loworder Quasidiffusion (QD) equations are discretized by the second-order scheme. To reduce non-monotonicity of the low-order solution we apply a monotonization procedure to the discretized time-dependent low-order equations based on the Limited-Trapezoidal method. Numerical results of the Fleck-Cummings test are presented to demonstrate performance of the developed mixed-order time integration scheme for the multilevel system of high-order and low-order QD equations. We use this TRT test problem to analyze the convergence in time of the mixed-order scheme. (C) 2020 Elsevier Inc. All rights reserved.