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has been cited by the following article:
TITLE: Postshock Oscillations on Non-Uniform Mesh
AUTHORS: Fuxing Hu
KEYWORDS: Nonuniform Mesh, Hyperbolic Conservation Laws, Postshock Oscillation
JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.5 No.2, February 24, 2017
ABSTRACT: An investigation of postshock oscillations on non-uniform grids is performed in this paper. These oscillations are generated as shock passes through the grid interfaces. The LLF scheme is checked for 1D and 2D problems on the discontinuous grids. Oscillations are observed only for nonlinear systems and the solutions of the scalar conservation laws and linear systems behave logically. The integral curves suggest underlying properties of these oscillations. The results of the paper reveal a flaw that adaptive methods for conservation laws have to refine grids at each time step.