TY - JOUR
T1 - A Numerical Study for the Performance of the WENO Schemes Based on Different Numerical Fluxes for the Shallow Water Equations
JO - Journal of Computational Mathematics
VL - 6
SP - 807
EP - 825
PY - 2010
DA - 2010/12
SN - 28
DO - http://doi.org/10.4208/jcm.1001-m3122
UR - https://global-sci.org/intro/article_detail/jcm/8551.html
KW - Numerical flux, WENO finite volume scheme, Shallow water equations, High
order accuracy, Approximate Riemann solver, Runge-Kutta time discretization.
AB - <p style="text-align: justify;">In this paper we investigate the performance of the weighted essential non-oscillatory (WENO) methods based on different numerical fluxes, with the objective of obtaining better performance for the shallow water equations by choosing suitable numerical fluxes. We consider six numerical fluxes, i.e., Lax-Friedrichs, local Lax-Friedrichs, Engquist-Osher, Harten-Lax-van Leer, HLLC and the first-order centered fluxes, with the WENO finite volume method and TVD Runge-Kutta time discretization for the shallow water equations. The detailed numerical study is performed for both one-dimensional and two-dimensional shallow water equations by addressing the issues of CPU cost, accuracy, non-oscillatory property, and resolution of discontinuities.</p>