A&a Manuscript No. Astronomy and Astrophysics the Consistent Multi--uid Advection Method

Simple modiications for higher-order Godunov-type diierence schemes are presented which allow for accurate advection of multi-uid ows in hydrodynamic simulations. The constraint that the sum of all mass fractions has to be equal to one in every computational zone throughout the simulation is fulllled by renormalizing the mass fractions during the advection step. The proposed modiication is appropriate for any diierence scheme written in conservation form. Unlike other commonly used methods it does not violate the conservative character of the advection method. A new steepening mechanism, which is based on modiication of interpolation prooles, is used to reduce numerical diiusion across composition discontinuities. Additional procedures are described, which are necessary to enforce monotonicity. Several numerical experiments are presented which demonstrate the capability of our Consistent Multi-uid Advection (CMA) method in case of smooth and discontinuous distributions of uid phases and under diierent hydrodynamic conditions. It is shown that due to the reduced diiusivity of the proposed scheme the abundance of some heavy elements obtained from hydrodynamic simulations of type II supernova explosions can change by a factor of a few in the most extreme cases.