Improvement on Spherical Symmetry in Two-Dimensional Cylindrical Coordinates for a Class of Control Volume Lagrangian Schemes (Communications in Computational Physics, 2020)
In [14], Maire developed a class of cell-centered Lagrangian schemes forsolving Euler equations of compressible gas dynamics in cylindrical coordinates. Theseschemes use a node-based discretization of the numerical fluxes. The control volume version has several distinguished properties, including the conservation of mass,momentum and total energy and compatibility with the geometric conservation law(GCL). However, it also has a limitation in that it cannot preserve spherical symmetryfor one-dimensional spherical flow. An alternative is also given to use the first orderarea-weighted approach which can ensure spherical symmetry, at the price of sacrificing conservation of momentum. In this paper, we apply the methodology proposed inour recent work [8] to the first order control volume scheme of Maire in [14] to obtainthe spherical symmetry property. The modified scheme can preserve one-dimensionalspherical symmetry in a two-dimensional cylindrical geometry when computed on anequal-angle-zoned initial grid, and meanwhile it maintains its original good propertiessuch as conservation and GCL. Several two-dimensional numerical examples in cylindrical coordinates are presented to demonstrate the good performance of the schemein terms of symmetry, non-oscillation and robustness properties.