A new class of high-order weighted essentially non-oscillatory schemes for hyperbolic conservation laws

In this paper, a class of even order WENO schemes, including fourth-order, sixth-order and eighth-order schemes, are presented in finite volume framework for hyperbolic conservation laws. Instead of two upwind stencils in the classical WENO reconstruction [10] for each cell interface, a common symmetrical stencil is used in the reconstruction of the variables at its both sides. For each cell interface, the 2rth order scheme shares the same number of cell averaged values with the (2r−1)th order classical WENO scheme. To suppress the spurious oscillation and improve the resolution in the region with discontinuities, a convex combination and a nonlinear weighting strategy are given with the unequal degree polynomials from the candidate sub-stencils. In smooth region, the current schemes achieve one order of improvement in accuracy compared with the classical WENO schemes. A variety of numerical tests are presented to validate the performance of the current schemes. Complex flow structures and discontinuities can be well resolved, and the robustness is as good as that of the classical WENO schemes.