  Simple modifications for higher-order Godunov-type difference schemes are
presented which allow for accurate advection of multi-fluid flows 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
fulfilled 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 the
conservative character of the advection method. A new steepening mechanism,
which is based on modification of interpolation profiles, is used to reduce
numerical diffusion 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-fluid Advection (CMA) method in case of smooth and discontinuous
distributions of fluid phases and under different hydrodynamic conditions. It
is shown that due to the reduced diffusivity 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.
