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).
Highlights
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
The semi-Lagrangian methods are popularly used in weather prediction [1] [2] and simulation of the Vlasov equations [3] [4] [5] [6], and so on
This paper aims to combine the finite volume semi-Lagrangian WENO method with flux vector splitting
Summary
The semi-Lagrangian methods are popularly used in weather prediction [1] [2] and simulation of the Vlasov equations [3] [4] [5] [6], and so on. These methods solve the problems with a characteristic tracing algorithm. The semi-Lagrangian methods (combined wih WENO reconstruction [7] [8]) used to solve hyperbolic problems are presented in [9] [10] [11]. In [10], the authors proposed a finite volume semi-Lagrangian WENO scheme for advection problems.
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