Title: A simple and efficient finite volume WENO method for hyperbolic conservation laws.
Abstract: In this presentation, we present simple high order weighted essentially non- oscillatory (WENO) schemes to solve hyperbolic conservation laws. The main advantages of these schemes are their compactness, robustness and good convergence property for solving steady state problems. Comparing with the classical WENO schemes by G.-S. Jiang and C.-W. Shu (J. Comput. Phys., 126 (1996), 202-228), there are two major advantages of the new WENO schemes. The first, the associated optimal linear weights are independent on topological structure of meshes, can be any positive numbers with only requirement that their summation equals to one. The second is that the new scheme is more compact and efficient than the schemes by Jiang and Shu. Extensive numerical results are provided to illustrate the good performance of these new WENO schemes.