论文标题
用于球形几何的弱压缩流的有效算法
An efficient algorithm for weakly compressible flows in spherical geometries
论文作者
论文摘要
这项研究提出了一种基于隐式拆分方法，用于在几乎不可压缩且弱可压缩的方案中对球形壳中可压缩流的算法。该方法保留了理论上预期的收敛速率，并且对于特征马赫数的极小值，该方法保持稳定。 MAC模具上交错的空间离散化，通常以数值方法用于不可压缩的Navier-Stokes方程，发现以非保守形式以原始变量为单位的非保守形式编写的可压缩Navier-Stokes方程非常方便。这种方法有助于避免没有任何人工稳定项的高频振荡。还实施了降低分裂误差的非线性PICARD迭代，以允许一个人获得完全非线性方程系统的解决方案。这些结果以及出色的并行性能证明了大气和海洋流的大规模高分辨率高性能模拟中方向分裂方法的生存能力。
This study proposes an algorithm for modeling compressible flows in spherical shells in nearly incompressible and weakly compressible regimes based on an implicit direction splitting approach. The method retains theoretically expected convergence rates and remains stable for extremely small values of the characteristic Mach number. The staggered spatial discretization on the MAC stencil, commonly used in numerical methods for incompressible Navier-Stokes equations, was found to be convenient for the discretization of the compressible Navier-Stokes equations written in the non-conservative form in terms of the primitive variables. This approach helped to avoid the high-frequency oscillations without any artificial stabilization terms. Nonlinear Picard iterations with the splitting error reduction were also implemented to allow one to obtain a solution of the fully nonlinear system of equations. These results, alongside excellent parallel performance, prove the viability of the direction splitting approach in large-scale high-resolution high-performance simulations of atmospheric and oceanic flows.
