@Article{CiCP-11-4,
author = {},
title = {Improvement on Spherical Symmetry in Two-Dimensional Cylindrical Coordinates for a Class of Control Volume Lagrangian Schemes},
journal = {Communications in Computational Physics},
year = {2012},
volume = {11},
number = {4},
pages = {1144--1168},
abstract = {<p style="text-align: justify;">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, 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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.030710.131210s},
url = {https://global-sci.com/article/80734/improvement-on-spherical-symmetry-in-two-dimensional-cylindrical-coordinates-for-a-class-of-control-volume-lagrangian-schemes}
}