Volume 11, Issue 4
Improvement on Spherical Symmetry in Two-dimensional Cylindrical Coordinates for a Class of Control Volume Lagrangian Schemes

Juan Cheng and Chi-Wang Shu

10.4208/cicp.030710.131210s

Commun. Comput. Phys., 11 (2012), pp. 1144-1168.

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  • Abstract

In [14], Maire developed a class of cell-centered Lagrangian schemes for solving Eulerequationsofcompressiblegasdynamicsincylindricalcoordinates. 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-zonedinitial grid, and meanwhile it maintains 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. 

  • History

Published online: 2012-04

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