Finite difference and finite volume ghost multi-resolution WENO schemes with increasingly higher order of accuracy.

This article provides the high-order finite difference and finite volume ghost multi-resolution weighted essentially non-oscillatory (GMR-WENO) schemes for solving hyperbolic conservation laws on structured meshes. We only utilize the information defined on one big central spatial stencil without introducing any equivalent multi-resolution representations. These GMR-WENO schemes utilize orthogonal Legendre basis to construct high degree polynomials of big central spatial stencils and use a L 2 projection methodology to obtain a series of ghost low degree polynomials whose degree could gradually range from the highest degree to the zeroth degree. Each of these GMR-WENO schemes only utilizes one big central spatial stencil to achieve arbitrary high-order accuracy in smooth regions and could gradually reduce to the first-order accuracy nearby strong discontinuities. The linear weights of such GMR-WENO schemes can be any positive numbers with a summation of one. This is the first time that only one central spatial stencil is utilized in designing high-order finite difference and finite volume WENO schemes. These GMR-WENO schemes have a simple construction and can easily achieve arbitrary high-order accuracy in higher dimensions. Benchmark examples are provided to demonstrate the efficiency of these GMR-WENO schemes. [ABSTRACT FROM AUTHOR]