83 / 2019-09-30 19:04:47

A Generalized Symmetric Third-Order Weighted Essentially Non-Oscillatory Scheme

WENO,low dissipation,hyperbolic conservation laws,smoothness indicator

In this paper, the adaptive central-upwind 4th-order WENO4-CU scheme is extended from Ref.[5] first. Then, we propose a generalized symmetric third-order scheme with low dissipation, sharp shock-capturing capability and good robustness. Improvements contain two parts as follows. Firstly, a downwind candidate stencil is added to the third-order upwind WENO scheme. The stencils of the symmetric schemes are presented in Fig. 1. Secondly, a new fourth-order global smoothness indicator is devised in the nonlinear weighting procedure which is similar to those of WENO3-Z and WENO4-CU. Numerical results of the double Mach reflection problem computed by different WENO schemes are shown in Fig. 2. Note that the proposed WENO3-LS scheme has a improved result compared with original WENO3-JS and WENO3-Z, and it has comparable resolution with WENO5-JS scheme.