A class of high-order weighted compact central schemes for solving hyperbolic conservation laws

We propose a class of weighted compact central schemes for solving hyperbolic conservation laws. The linear version can be considered as high-order extension the Lax–Friedrichs scheme and element solution scheme. On every cell, is approximated by Pth-order polynomial which all DOFs are stored updated separately. cell average classical finite volume constructed based on space-time staggered meshes such that fluxes continuous across interfaces adjacent control volumes and, therefore, local Riemann problem bypassed. kth-order spatial derivatives difference (k?1)th-order at vertices. All information calculated Cauchy–Kovalewski procedure. By doing so, able to achieve arbitrarily uniform stencil consisting only neighboring cells with one explicit time step. In order capture discontinuities without spurious oscillations, essentially non-oscillatory type limiter tailor-made schemes. preserves compactness accuracy schemes' accuracy, robustness, efficiency verified several numerical examples scalar laws compressible Euler equations.