A central-upwind incremental-stencil weighted essentially non-oscillatory scheme based on Euclidean norm regularization for compressible flows

For weighted essentially non-oscillatory (WENO) schemes, assembling a set of candidate stencils with incremental width other than the same width stencils can not only enhance the numerical stability but also improve the wave-resolution property. In this work, a 6-point central-upwind incremental-stencil WENO scheme is proposed to improve the performance of the scheme for the simulation of compressible flows. First, a 6-point framework by adopting 2-, 3-, and 4-point candidate stencils is devised for flux reconstruction. To address the excessive numerical dissipation induced by the discrepancy of the smoothness indicator between high-order and low-order stencils, Euclidean norm (L2-norm) regularization strategy is introduced to modulate the weights of incremental stencils. In addition, the background linear scheme is kept dissipative by cooperating with an upwind term to suppress numerical oscillations. Then, a linear upwind scheme with adaptive numerical dissipation is devised and adopted to hybrid with the proposed scheme to further improve the computational efficiency and the resolution. A set of benchmark cases involving strong discontinuities and broadband length scales are simulated to demonstrate the stability, high resolution, and efficiency of the proposed scheme.