Interpolatory conservative-characteristic scheme with improved dispersion properties for computational fluid dynamics

Conservative-characteristic schemes for the numerical solution of systems of hyperbolic equations combine the advantages of shock-capturing conservative methods and the method of characteristics. They operate with two types of variables: conservative and flux. Conservative variables have the meaning of mean values, refer to the middle of the cells, and are calculated using the finite volume method. The flux variables determine the fluxes on the faces of computational cells and are calculated using the characteristic form of equations and local Riemann invariants. This part of the algorithm allows various implementations, on which the dissipative and dispersion properties of the algorithms depend. For example, in the CABARET scheme, the flux variables are calculated by linear extrapolation of local invariants, but there are also schemes with interpolation of invariants and their subsequent transfer along the characteristics (active flux schemes). In the latter case, various options are also possible. This article is devoted to the results of the study of a possible variant of interpolatory conservative-characteristic schemes for systems of hyperbolic equations.