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).