Monotone approximation of a scalar conservation law based on the CABARET scheme in the case of a sign-changing characteristic field

Аннотация

The monotonicity of the CABARET scheme approximating a quasilinear scalar conservation law with a convex flux is analyzed. Monotonicity conditions for this scheme are obtained in domains where the propagation velocity of characteristics of the approximated conservative equation is of constant sign and near sonic lines, at which the propagation velocity of characteristics changes its sign. Test computations illustrating these properties of the CABARET scheme are presented.