About one variant of multidimensional extension of the “cabaret” scheme

To solve advection equation in divergent form the new variant of conservative multidimensional extension of “cabaret” (upwind leapfrog) scheme is proposed. In two dimensions on the rectangular grid two and three layered variants of the scheme are derived. The stability properties as well as spectral characteristics of the scheme are analyzed. The results of numerical tests show robustness of the proposed scheme and also improvement in accuracy over leapfrog scheme. Comparison with known multidimensional extension of the “cabaret” scheme and further possibilities to improve this scheme are discussed.