地球外核热对流运动的区域分解多重网格并行数值模拟

旋转球层中热对流运动的数值模拟是地球发电机模型的重要组成部分，对研究地球发电机作用机理具有重要意义.本文设计一个基于国产超级计算平台并行性能良好的地球外核热对流运动并行数值模型.时间积分方案采用与Crank-Nicolson格式和二阶Adams-Bashford公式相结合的近似分解分步法，空间离散基于立方球网格的二阶精度有限体积格式.所得到的两个大规模稀疏线性代数方程组采用带预处理的Krylov子空间迭代法进行求解.为加速迭代求解过程及提高并行性能，迭代过程采用区域分解多重网格的多层限制型加法Schwarz预处理子，减少了求解程序的计算时间，提高了数值模型的并行性能，模型被很好地扩展到上万处理器核数.数值模拟结果与基准模型算例0的参考值吻合得很好.

Parallel Numerical Simulations of Thermal Convection in the Earth's Outer Core Based on Domain Decomposition and Multigrid

Numerical simulations of thermal convection in a rotating spherical shell play an important role in dynamo models. In this paper, we present a parallel numerical model with high performance for the Earth's outer core convection based on a homegrown supercomputer. An approximate factorization fractional method combined with Crank-Nicolson scheme and second-order Adams-Bashford formula is employed for temporal integration. Spatial terms are discretized by a second-order finite volume scheme based on cubed-sphere grid. Two resultant large sparse linear algebraic equations are solved by preconditioned Krylov subspace iterative method. To accelerate convergence rate and improve parallel performance, linear solver is preconditioned with multilevel restricted additive Schwarz preconditioner based on domain decomposition and multigrid. The preconditioner reduces compute time and improve parallel performance of the solvers, which scales well to over ten thousand processor cores. Numerical results are in good agreement with reference solutions of the benchmark Case 0.