自适应结构网格上扩散方程隐式时间积分算法及其应用

提出一种自适应结构网格(SAMR)上求解扩散方程的隐式时间积分算法.该算法从粗网格到细网格逐层进行时间积分,通过多层迭代同步校正保证粗细界面的流连续和计算区域的扩散平衡.分析算法复杂度,并给出评估算法低复杂度的准则.典型算例表明,相对于一致加密情形,本文算法能够在保持相同计算精度的前提下,大幅度降低网格规模和计算量,且具有低复杂度.将算法应用于辐射流体力学数值模拟中非线性扩散方程组求解,相对于一致加密网格,SAMR计算将计算量下降一个量级以上,计算效率提高33.2倍.

An Implicit Time-integration Algorithm for Diffusion Equations with Structured AMR and Applications

We consider solution of diffusion equations using structured adaptive mesh refinement(SAMR).In SAMR hierarchy, each level is organized as a union of uniform rectangular patches.An implicit time-integration algorithm with temporal refinement strategy is shown.In the algorithm,timestepping advances from the coarsest level to the finest level sequentially,and a multilevel synchronization process is required for fixing fluxes dismatch at coarse-fine interface.A criterion for algorithm complexity is introduced. Numerical results show validation and performance of the algorithm.Finally,the algorithm is applied to radiation hydrodynamics simulations,where nonlinear non-equilibrium radiation diffusion equations are solved.Simulation result shows that,compared with uniform refinement mesh,performance of the method is improved by 33 times.