A numerical study of the performance of alternative weighted ENO methods based on various numerical fluxes for conservation law

In this paper, we systematically investigate the performance of the weighted essential non-oscillatory (WENO) methods based on various numerical fluxes for the nonlinear hyperbolic conservation law. Our objective is enhancing the performance for the conservation laws through picking out the suitable numerical fluxes. We focus our attention entirely on the comparison of eight numerical fluxes with the fifth-order accurate finite difference WENO methods and third-order accurate TVD Runge–Kutta time discretization for hyperbolic conservation laws. In addition, we give their implementation based on a new form framework of flux which we used in [9] and was proposed by Shu and Osher in [16]. The detailed numerical study is mainly implemented for the one dimensional system case, including the discussion of the CPU cost, accuracy, non-oscillatory property, and resolution of discontinuities. Numerical tests are also performed for two dimensional systems.