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

• DOI: 10.4208/cicp.030710.131210s
• Publication Date: 2012-05-22T08:40:10Z
• Authors: Juan Cheng; Chi-Wang Shu
• Keywords: Circular symmetry; Conservation law; Control volume

Abstract In, Maire developed a class of cell-centered Lagrangian schemes for solving Euler equations compressible gas dynamics in cylindrical coordinates. These use node-based discretization the numerical fluxes. The control volume version has several distinguished properties, including conservation mass, momentum and total energy compatibility with geometric law (GCL). However it also limitation that cannot preserve spherical symmetry one-dimensional flow. An alternative is given to first order area-weighted approach which can ensure symmetry, at price sacrificing momentum. In this paper, we apply methodology proposed our recent work scheme obtain property. modified two-dimensional geometry when computed on an equal-angle-zoned initial grid, meanwhile maintains its original good properties such as GCL. Several examples coordinates are presented demonstrate performance terms non-oscillation robustness properties.