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-or...

The development of flux-vector splitting through the 1970s and 1980s is reviewed. Attention is given to the diffusive nature of flux-vector splitting, which makes it an undesirable technique for approximating the inviscid fluxes in a Navier-Stokes solver. Several proposed improvements, including a brandnew one, are discussed and illustrated by a simple, yet revealing, numerical test case. Final...

Co-Investigators, University of Michigan: Natasha Andronova, Atmospheric, Oceanic and Space Sciences Krzysztof J. Fidkowski, Aerospace Engineering Bruce Fryxell, Atmospheric, Oceanic and Space Sciences Tamas I. Gombosi, Atmospheric, Oceanic and Space Sciences Eric Johnsen, Mechanical Engineering and Applied Mechanics Smadar Karni, Mathematics Carolyn C. Kuranz, Atmospheric, Oceanic and Space Sc...

A gas-kinetic flux splitting method is developed for the ideal magnetohydrodynamics (MHD) equations. The new scheme is based on the direct splitting of the flux function of the MHD equations with the inclusion of “particle” collisions in the transport process. Consequently, the artificial dissipation in the new scheme is greatly reduced in comparison with the MHD flux vector splitting method. N...