CIP/multi-moment finite volume method for Euler equations: A semi-Lagrangian characteristic formulation

An accurate algorithm for the hyperbolic equations has been proposed by combining the constrained interpolation profile/multi-moment finite volume method (CIP/MM FVM) with the characteristic theory. Two types of moments, i.e. the point value (PV) at cell boundary of each mesh element and the volume-integrated average (VIA) over each mesh cell of a physical field, are treated as the model variables and updated independently in time. The interpolation that uses both PV and VIA is reconstructed for each Riemann invariant of the hyperbolic conservation laws. The PVs are then updated by semi-Lagrangian schemes along the characteristic curves, while the VIAs are computed by formulations of flux form, where the numerical fluxes are evaluated by averaging the physical fields over the characteristic curves. The Runge–Kutta type schemes are used for integrating the trajectory equations based on the characteristic speeds to improve the accuracy in time.The numerical procedure for the one-dimensional Euler conservation laws is described in detail in this paper. Number of benchmark tests are presented. The numerical results show that the present method is accurate and competitive to other existing methods.