Improvement on Spherical Symmetry in Two-Dimensional Cylindrical Coordinates for a Class of Control Volume Lagrangian Schemes

In[14],Maire developed a class of cell-centered Lagrangian schemes for solving Euler equations of compressible gas dynamics in cylindrical coordinates.These schemes 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 symmetry for one-dimensional spherical flow.An alternative is also given to use the first order area-weighted approach which can ensure spherical symmetry,at the price of sacrificing conservation of momentum.In this paper,we apply the methodology proposed in our recent work[8]to the first order control volume scheme of Maire in[14]to obtain the spherical symmetry property.The modified scheme can preserve one-dimensional spherical symmetry in a two-dimensional cylindrical geometry when computed on an equal-angle-zoned initial grid,andmeanwhile itmaintains its original good properties such as conservation and GCL.Several two-dimensional numerical examples in cylindrical coordinates are presented to demonstrate the good performance of the scheme in terms of symmetry,non-oscillation and robustness properties.