2025 , Volume 30, № 6, p.56-75

In this paper we study the monotonicity of the CABARET scheme which is aimed to approximate a general form of hyperbolic system of conservation laws, i.e., system that does not admit an invariant form. The main purpose of this paper is to construct a modification (MCABARET) of this scheme which preserves the monotonicity of the difference solution of the examined system with respect to the invariants in the linear approximation. Comparative analysis of the accuracy of these modifications for the calculation of the Sod problem due to the initial discontinuous decay in a polytropic gas is carried out. The calculations using the MCABARET scheme does not show oscillations of velocity and pressure values on the shock wave, while the CABARET schemes predict the contrary. Further, the comparison of schemes on the modified Soda problem was carried out. The change of sign in front of the velocity of the characteristics of the first family is the difference between our model and the classical one. We stress out that the MCABARET scheme approximates the self similar exact solution with high accuracy. Numerical solutions obtained by CABARET schemes predict an unstable strong discontinuity formed in the right part of the centred rarefaction wave of the exact solution. It occurs because these schemes do not satisfy the difference analogue of the entropy inequality, which ensures the absence of unstable strong discontinuities.