CABARET scheme’s modification ensuring its high accuracy on local extrema

详细

It is demonstrated that the standard flow-variables’ correction required for the monotonicity of the CABARET scheme reduces its accuracy near local extrema. A modified correction of the flows is proposed; it retains the strong monotonicity of the CABARET scheme for Courant numbers r ∈ (0,0.5], and thus ensures its high accuracy near local extrema. The results of the test computations of discontinuous solutions of a nonlinear transport equation are presented; these results illustrate the advantages of the modified scheme.