A variant of the multidimensional generalization of the cabaret scheme
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To solve the advection equation in divergent form, a new variant of the conservative multidimensional extension of the cabaret scheme is proposed. In the two-dimensional case, the two- and three-layered variants of the scheme are derived on a rectangular grid. The stability properties of the scheme and its dissipative and dispersion characteristics are analyzed. The results of the numerical tests show the robustness of the proposed scheme and the improved accuracy compared to the leapfrog scheme. This scheme is compared with the known multidimensional extension of the cabaret scheme, and further possibilities for its improvement are discussed.
KeywordsFlux Variable Rectangular Grid Advection Equation Conservative Variable Courant Number
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