An efficient modified WENO scheme based on the identification of inflection points

In this paper, a new modified fifth-order weighted essentially non-oscillatory (WENO) scheme is proposed by introducing a switching principle based on the identification of inflection points. The switching principle adjusts the scheme between the linear upwind scheme and the WENO-M scheme automatically. If there is one or more inflection points located in the large reconstruction stencil, the WENO-M procedure is applied to reconstruct the numerical flux, instead of the classical WENO scheme; otherwise, the linear upwind scheme is used. The new scheme is more efficient due to the identification of the inflection points, and has higher numerical accuracy and resolution due to the usage of WENO-M procedure. A set of benchmark problems are conducted and analyzed to verify the performance enhancement. The extreme shock tube problem of Leblanc is computed to demonstrate the robustness of the new scheme.