An efficient algorithm for weakly compressible flows in spherical geometries,International Journal for Numerical Methods in Fluids

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An efficient algorithm for weakly compressible flows in spherical geometries
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2020-11-25 , DOI: 10.1002/fld.4932
Roman Frolov ₁ , Peter Minev ₂ , Aziz Takhirov ₃

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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.

中文翻译：

球形几何中弱可压缩流动的有效算法

本研究提出了一种基于隐式方向分裂方法对几乎不可压缩和弱可压缩状态下球壳中的可压缩流动进行建模的算法。该方法保留了理论上预期的收敛速度，并且对于特征马赫数的极小值保持稳定。MAC 模板上的交错空间离散化，常用于不可压缩 Navier-Stokes 方程的数值方法，被发现便于将非保守形式的可压缩 Navier-Stokes 方程离散化为原始变量。这种方法有助于在没有任何人工稳定项的情况下避免高频振荡。还实现了具有分裂误差减少的非线性 Picard 迭代，以允许获得完全非线性方程组的解。这些结果以及出色的并行性能证明了方向分裂方法在大气和海洋流动的大规模高分辨率高性能模拟中的可行性。

更新日期：2020-11-25

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