A new hybrid scheme for computing discontinuous solutions of hyperbolic equations

In this work, the hybrid scheme is analyzed. It was introduced earlier as a technique to monotonize bicompact schemes for hyperbolic equations and systems. Its imperfections are discussed. They include the disregard of the various behavior of solution components in the general case, monotonizing nature dependence on a system of units and on a scale of initial and boundary conditions; the lack of a priori estimations of the hybrid scheme tuned parameter. To eliminate these imperfections a new hybrid scheme is constructed. It involves the component-wise monotonization and the solution normalization. The correct normalization is obtained. The general algorithm for a priori estimation of the hybrid scheme parameter is proposed. Numerical examples for the hybrid bicompact scheme with the first-order explicit upwind scheme monotonizer are considered.