The consistent multi-fluid advection method

Simple modifications for higher-order Godunov-type difference schemes are p resented which allow for accurate advection of multi-fluid flows in hydrody namic simulations. The constraint that the sum of all mass fractions has to be equal to one in every computational zone throughout the simulation is f ulfilled by renormalizing the mass fractions during the advection step. The proposed modification is appropriate for any difference scheme written in conservation form. Unlike other commonly used methods it does not violate t he conservative character of the advection method. A new steepening mechani sm, which is based on modification of interpolation profiles, is used to re duce numerical diffusion across composition discontinuities. Additional pro cedures are described, which are necessary to enforce monotonicity. Several numerical experiments are presented which demonstrate the capability of ou r Consistent Multi-fluid Advection (CMA) method in case of smooth and disco ntinuous distributions of fluid phases and under different hydrodynamic con ditions. It is shown that due to the reduced diffusivity of the proposed sc heme the abundance of some heavy elements obtained from hydrodynamic simula tions of type II supernova explosions can change by a factor of a few in th e most extreme cases.