Improvement of the weighted essentially nonoscillatory scheme based on the interaction of smoothness indicators

The weighted essentially nonoscillatory scheme is improved by introducing new smoothness indicators that evaluate the interactions among the classical smoothness indicators suggested by Jiang and Shu. The effect of the key parameters in the new smoothness indicators on the scheme is systematically investigated. The improved scheme has smaller dissipation with larger weight assignment to the discontinuous stencils and higher numerical accuracy with weights closer to the ideal weights. To verify the theory, benchmark problems governed by the linear transport equation, the 1-dimensional nonlinear Burgers equation, and the Euler equations are conducted and analyzed, respectively. Better computational performances both on numerical resolution and accuracy are shown in the comparisons with other classical weighted essentially nonoscillatory schemes.