High-order variable index weighted essentially non-oscillatory scheme for hyperbolic conservation law

In this paper, a new type of weighted essentially non-oscillatory scheme with variable index (VWENO) is obtained. The index can adaptively adjust with the solution, to ensure that the VWENO scheme uses optimal weights in smooth regions, while non-linear weights are used in less smooth regions. Theoretical and numerical results show that the variable index can make the result of VWENO achieve the optimal weights in the smooth regions without amplifying the weight of less smooth sub-stencils containing discontinuities. Theoretical and numerical calculation experiments show that the new scheme's shock capture capability and the resolution of complex process structures are significantly better than WENO-JS and WENO-Z.