A direction splitting scheme for Navier–Stokes–Boussinesq system in spherical shell geometries,International Journal for Numerical Methods in Fluids

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A direction splitting scheme for Navier–Stokes–Boussinesq system in spherical shell geometries
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-09-15 , DOI: 10.1002/fld.5043
Aziz Takhirovb ₁ , Roman Frolovc ₂ , Peter Mineva ₃

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This article introduces a second-order direction splitting method for solving the incompressible Navier–Stokes–Boussinesq system in a spherical shell region. The equations are solved on overset Yin–Yang grids, combined with spherical coordinate transforms. This approach allows to avoid the singularities at the poles and keeps the grid size relatively uniform. The downside is that the spherical shell is subdivided into two equally sized, overlapping subdomains that requires the use of Schwarz-type iterations. The temporal second-order accuracy is achieved via an artificial compressibility scheme with bootstrapping. The spatial discretization is based on second-order finite differences on the Marker-And-Cell stencil. The entire scheme is implemented in parallel using a domain decomposition iteration and a direction splitting approach for the local solves. The stability, accuracy, and weak scalability of the method is verified on a manufactured solution of the Navier–Stokes–Boussinesq system while its practicality is demonstrated on the natural convection problem in the gap between two concentric spheres.

中文翻译：

球壳几何中 Navier-Stokes-Boussinesq 系统的方向分裂方案

本文介绍了求解球壳区域不可压缩 Navier-Stokes-Boussinesq 系统的二阶方向分裂方法。方程在重叠阴阳网格上求解，并结合球坐标变换。这种方法可以避免极点处的奇点并保持网格尺寸相对均匀。缺点是球壳被细分为两个大小相同、重叠的子域，这需要使用 Schwarz 类型的迭代。时间二阶精度是通过带有自举的人工压缩方案实现的。空间离散化基于 Marker-And-Cell 模板上的二阶有限差分。整个方案是使用域分解迭代和局部求解的方向分裂方法并行实现的。该方法的稳定性、准确性和弱可扩展性在 Navier-Stokes-Boussinesq 系统的制造解决方案上得到验证，同时在两个同心球之间的间隙中的自然对流问题上证明了其实用性。

更新日期：2021-11-15

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