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Kim, S., Kim, C., Rho, O. and Hong, S. (2003) Cures for the Shock Instability: Development of a Shock-Stable Roe Scheme. Journal of Computational Physics, 185, 342-374.

has been cited by the following article:

• TITLE: The Approximated Semi-Lagrangian WENO Methods Based on Flux Vector Splitting for Hyperbolic Conservation Laws

  AUTHORS: Fuxing Hu

  KEYWORDS: Semi-Lagrangian Method, WENO Scheme, Flux Splitting

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.7 No.1, March 31, 2017

  ABSTRACT: The paper is devised to combine the approximated semi-Lagrange weighted essentially non-oscillatory scheme and flux vector splitting. The approximated finite volume semi-Lagrange that is weighted essentially non-oscillatory scheme with Roe flux had been proposed. The methods using Roe speed to construct the flux probably generates entropy-violating solutions. More seriously, the methods maybe perform numerical instability in two-dimensional cases. A robust and simply remedy is to use a global flux splitting to substitute Roe flux. The combination is tested by several numerical examples. In addition, the comparisons of computing time and resolution between the classical weighted essentially non-oscillatory scheme (WENOJS-LF) and the semi-Lagrange weighted essentially non-oscillatory scheme (WENOEL-LF) which is presented (both combining with the flux vector splitting).