Compact Accurately Boundary-Adjusting high-REsolution Technique for fluid dynamics

A novel high-resolution numerical method is presented for one-dimensional hyperbolic problems based on the extension of the original Upwind Leapfrog scheme to quasi-linear conservation laws. The method is second-order accurate on non-uniform grids in space and time, has a very small dispersion error and computational stencil defined within one space–time cell. For shock-capturing, the scheme is equipped with a conservative non-linear correction procedure which is directly based on the maximum principle. Plentiful numerical examples are provided for linear advection, quasi-linear scalar hyperbolic conservation laws and gas dynamics and comparisons with other computational methods in the literature are discussed.