一种求解三维热辐射输运方程的整体预处理迭代方法及并行计算  

A Monolithic Preconditioned Iterative Solver and Parallel Computing for Three-dimensional Thermal Radiation Transport Equation

作　　者：李凌霄 翟传磊[1] 谢辉 施意[1] LI Lingxiao;ZHAI Chuanlei;XIE Hui;SHI Yi(Institute of Applied Physics and Computational Mathematics,Beijing 100094,China)

机构地区：[1]北京应用物理与计算数学研究所,北京100094

出　　处：《计算物理》2021年第3期269-279,共11页Chinese Journal of Computational Physics

基　　金：挑战计划(TZ2016002);国家自然科学基金(11901042、11901043);中物院创新发展基金(CX20200026)资助项目;。

摘　　要：为三维灰体热辐射输运方程的隐式离散纵标方法发展一个整体预处理迭代方法并研制并行程序。该方法采用组装线性代数方程组策略,同时求出所有离散方向上的辐射强度。借助预处理的Krylov子空间迭代法,避免复杂网格上扫描算法可能遇到的死锁问题,能够提高健壮性和计算效率。空间离散上采用一阶迎风有限体积格式。数值实验测试变形六面体网格上的收敛率、评估预处理迭代方法的性能并计算辐射和物质的耦合问题,给出三维弯管和黑腔问题的模拟结果,验证程序的正确性和方法的适应性。We present a monolithic preconditioned iterative solver for implicit discrete ordinate equations of three-dimensional grey thermal radiation transport and parallel codes are developed.A strategy of assembling linear algebraic systems is used to obtain radiation intensity in all discrete directions simultaneously.With preconditioned Krylov subspace iterative methods,the solver avoids possible mesh cycles in complex grids associated with sweep algorithms,which improves robustness and computational efficiency.First order upwind finite volume scheme is used for space discretization.Numerical experiments verify convergence rate on distorted hexahedral grids and assess performance of preconditioned iterative methods.Problems with coupled radiation and matter are simulated.Simulation results of three-dimensional crooked pipe and hohlraum problems are shown.It shows validity of the codes and flexibility of the method.

关 键 词：三维辐射输运方程 预处理Krylov子空间方法 离散纵标方法 并行计算 

分 类 号：O242.1[理学—计算数学]