On shock-capturing schemes using artificial wind

We introduce and apply a new way for the construction of efficient non-osci llatory shock-capturing schemes for fluid dynamic and magneto-hydro-dynamic simulations. The basic idea is to solve the governing equations in differe nt steadily moving frames of reference chosen in such a way that the flow w ould be supersonic there resulting in simple upwind formulas for fluxes acr oss control volume faces. An extra velocity (artificial mind) is added to t he velocity of the flow under simulation when the system of coordinates is changed. The approach allows to simplify existing schemes and to get new mo difications. Test problems demonstrate that the derived schemes provide acc urate results while being simple and efficient.