Bicompact schemes for multidimensional hyperbolic equations on Cartesian meshes with solution-based AMR

High-order bicompact schemes for hyperbolic equations on Cartesian meshes with solution-based adaptive mesh refinement are constructed. The algorithm for implementation of these schemes on such meshes is described in detail. A new solution-based criteria of mesh refinement is proposed. Bicompact schemes with this refinement criteria are tested on the two-dimensional problem of compactly supported pulse advection and the two-dimensional Sedov blast wave problem. It is shown, that the design of bicompact schemes allows them to be implemented on meshes of such class with good accuracy of the computed solution ensured.