  The seven-equation model is a compressible multiphase formulation that allows
for phasic velocity and pressure disequilibrium. These equations are solved
using a diffused interface method that models resolved multiphase flows. Novel
extensions are proposed for including the effects of surface tension,
viscosity, multi-species, and reactions. The allowed non-equilibrium of
pressure in the seven-equation model provides numerical stability in strong
shocks and allows for arbitrary and independent equations of states. A discrete
equations method (DEM) models the fluxes. We show that even though stiff
pressure- and velocity-relaxation solvers have been used, they are not needed
for the DEM because the non-conservative fluxes are accurately modeled. An
interface compression scheme controls the numerical diffusion of the interface,
and its effects on the solution are discussed. Test cases are used to validate
the computational method and demonstrate its applicability. They include
multiphase shock tubes, shock propagation through a material interface, a
surface-tension-driven oscillating droplet, an accelerating droplet in a
viscous medium, and shock-detonation interacting with a deforming droplet.
Simulation results are compared against exact solutions and experiments when
possible.
