三维强粘性地幔对流的拟压缩多重网格迭代算法
Multigrid iterative algorithm using pseudo-compressibility for three-dimensional mantle convection with strongly variable viscosity
摘要：
提出了一种求解粘性强变化的地幔对流问题的数值算法。采用多重网格法结合拟压缩性和局部时间步长技术，对高粘性不可压缩流体的质量守恒和动量守恒方程进行了迭代求解。该算法适用于大规模三维数值模拟，因为（i）不需要任何额外矩阵的内存存储，（ii）矢量化和并行化是直接的。该算法已应用于三维矩形区域有限体积离散的地幔对流模拟程序中。基准比较与以前的二维和三维的计算，包括温度和/或深度依赖的粘度显示，准确的结果成功地再现，即使是几个数量级的粘度变化的情况下。通过增加多重网格操作过程中的前后平滑计算，数值方法对粘性变化的鲁棒性可以得到显著提高，并且对于高达1 e10的全局粘性变化可以实现收敛。
英文摘要：
A numerical algorithm for solving mantle convection problems with strongly variable viscosity is presented. Equations for conservation of mass and momentum for highly viscous and incompressible fluids are solved iteratively by a multigrid method in combination with pseudo-compressibility and local time stepping techniques. This algorithm is suitable for large-scale three-dimensional numerical simulations, because (i) memory storage for any additional matrix is not required and (ii) vectorization and parallelization are straightforward. The present algorithm has been incorporated into a mantle convection simulation program based on the finite-volume discretization in a three-dimensional rectangular domain. Benchmark comparisons with previous two- and three-dimensional calculations including the temperature- and/or depth-dependent viscosity revealed that accurate results are successfully reproduced even for the cases with viscosity variations of several orders of magnitude. The robustness of the numerical method against viscosity variation can be significantly improved by increasing the pre- and post-smoothing calculations during the multigrid operations, and the convergence can be achieved for the global viscosity variations up to 1e10.
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