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.