Eulerian finite-volume methods for two-phase fluid flows modeled by the five-equation diffuse interface model are considered. The methods are developed based on an interface capturing approach and aimed to reduce numerical smearing of material interfaces.

To achieve this goal, a sub-cell interface reconstruction procedure used simple interface patterns is introduced. The proposed sub-cell interface structure is then used for calculating the numerical flux across cell faces bordering mixed cells with taking into account transport of the reconstructed interface.

This is performed with the Composite Riemann Problem (CRP) that involves both a point of initial discontinuity and a material contact point. A hybrid HLL-HLLC method is incorporated to approximate the solution of the CRP (to be not self-similar) with taking into account multiple wave interactions.

The numerical flux approximation based on this CRP solution strongly reduces the interface smearing region. Numerical experiments show the reduction of the interface region up to one computational cell in 1D calculations and up to a few cells in 2D tests.