论文标题
球形坐标中三维不可压缩流的有限差分方案
A finite-difference scheme for three-dimensional incompressible flows in spherical coordinates
论文作者
论文摘要
在这项研究中，我们开发了一种灵活，有效的数值方案，用于模拟球形坐标中的三维不可压缩流。 The main idea, inspired by a similar strategy as (Verzicco, R., Orlandi, P., 1996, A Finite-Difference Scheme for Three-Dimensional Incompressible Flows in Cylindrical Coordinates) for cylindrical coordinates, consists of a change of variables combined with a discretization on a staggered mesh and the special treatment of few discrete terms that remove the singularities of the Navier-Stokes equations at the球体中心和沿极轴。这种新方法还减轻了极性轴周围离散化所引入的时间步长限制，而球体中心仍然产生强大的限制，尽管只有非常不利的流程配置。 该方案在空间上是二阶精确的，可以通过计算数值示例与其他代码产生的相似结果或文献中获得的相似结果进行验证和验证。 该方法可以应对在整个球体，球形外壳和扇形中不变的流量，而没有任何变化，并且由于有限差异的灵活性，它可以采用通用的网格拉伸（在三个方向中的两个）和复杂的边界条件。
In this study we have developed a flexible and efficient numerical scheme for the simulation of three-dimensional incompressible flows in spherical coordinates. The main idea, inspired by a similar strategy as (Verzicco, R., Orlandi, P., 1996, A Finite-Difference Scheme for Three-Dimensional Incompressible Flows in Cylindrical Coordinates) for cylindrical coordinates, consists of a change of variables combined with a discretization on a staggered mesh and the special treatment of few discrete terms that remove the singularities of the Navier-Stokes equations at the sphere centre and along the polar axis. This new method alleviates also the time step restrictions introduced by the discretization around the polar axis while the sphere centre still yields strong limitations, although only in very unfavourable flow configurations. The scheme is second-order accurate in space and is verified and validated by computing numerical examples that are compared with similar results produced by other codes or available from the literature. The method can cope with flows evolving in the whole sphere, in a spherical shell and in a sector without any change and, thanks to the flexibility of finite-differences, it can employ generic mesh stretching (in two of the three directions) and complex boundary conditions.
