Seventh order compact-WENO scheme for hyperbolic conservation laws. (15th November 2018) - Guo, Yan; Shi, YuFeng
Highlights: Seventh order finite volume compact-WENO scheme is proposed for solving 1D and 2D hyperbolic conservation laws. The parametrized maximum principle preserving and the parametrized positivity satisfying flux limiter flux limiter is coupled with the scheme. The one dimensional HLLC flux function is used to compute the interface fluxes. High-resolution properties with compact stencil. Abstract: In this paper, we construct a new seventh-order finite volume compact weighted essentially non-oscillatory (WENO) scheme for solving one and two dimensional hyperbolic conservation laws. We extend the main idea of fifth-order finite volume compact-WENO scheme which comes from the original WENO schemes to construct the present seventh-order scheme, where fourth-order compact stencils will be combined with nonlinear weights to get seventh-order finite volume compact-WENO scheme. The parametrized maximum principle preserving flux limiter is coupled with the seventh-order compact-WENO scheme for solving scalar hyperbolic conservation laws and the parametrized positivity satisfying flux limiter is applied to the new scheme for solving compressible Euler equations to maintain positive density and pressure. The HLLC (Harten, Lax and van Leer) flux function is used to compute the interface fluxes in the finite volume formulation. A number of 1D and 2D numerical tests are performed to demonstrate the efficiency and high-resolution properties of the proposed high-order compact scheme.