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 the spherical or cylindrical coordinates. Solution of the 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.
The authors were supported by the Russian Foundation for Basic Research (project
no. 19-51-14002) and the Austrian Science Fund (FWF) (project no. I-4311).
Citation:
I. M. Kulikov, E. I. Vorobyov, I. G. Chernykh, V. G. Elbakyan, “Application of geodesic grids for modeling the hydrodynamic processes in spherical objects”, Sib. Zh. Ind. Mat., 23:4 (2020), 77–87; J. Appl. Industr. Math., 14:4 (2020), 672–680
This publication is cited in the following 3 articles:
Igor Kulikov, Igor Chernykh, Eduard Vorobyov, Vardan Elbakyan, Lyudmila Vshivkova, Communications in Computer and Information Science, 1413, Mathematical Modeling and Supercomputer Technologies, 2021, 307
Igor Kulikov, “Molecular cloud collapse to stellar densities: models on moving geodesic vs. unstructured tetrahedron vs. nested meshes”, J. Phys.: Conf. Ser., 2028:1 (2021), 012001
I. M. Kulikov, “On a computational model of gravitational hydrodynamics with consideration of the radiation transfer in the diffusion approximation using tetrahedral meshes”, J. Appl. Industr. Math., 15:2 (2021), 277–284