Abstract

We propose a new numerical method that bases on the mathematical apparatus of geodesic grids. This approach allows us to simulate spherical objects without any singularities that occur in using spherical or cylindrical coordinates. Solution of hyperbolic equations is described in detail. The method is expanded to solve the equations of hydrodynamics and tested on the Sedov point explosion problem. The numerical method and the approach to grid construction make it possible to compute a rotation invariant solution in Cartesian coordinates. This in turn allows us to use this approach effectively for simulating various spherical astrophysical objects.

中文翻译：

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测地线网格在球形物体水动力过程建模中的应用

摘要

我们提出了一种基于测地网格的数学方法的新数值方法。这种方法使我们可以模拟球形物体，而不会出现使用球形或圆柱坐标的任何奇异点。详细描述了双曲方程的解。对该方法进行了扩展以求解流体动力学方程，并针对Sedov点爆炸问题进行了测试。数值方法和网格构建方法使计算笛卡尔坐标系中的旋转不变解成为可能。反过来，这又使我们能够有效地使用这种方法来模拟各种球形天体物体。