Numerical method for 3D two-component isothermal compressible flows with application to digital rock physics

We propose a numerical algorithm for simulations of two-component viscous compressible isothermal flows with surface effects in 3D domains of complex shape with voxel representation of geometry. The basic mathematical model is the regularized system of Navier-Stokes-Cahn-Hilliard equations. Simulations of droplet spreading over a flat base and displacement of one liquid by another one in a pore space of real rock sample are carried out. The simulation results demonstrate the applicability and good efficiency of the used system of equations, the corresponding difference scheme, and its implementation algorithms for numerical solution of the considered class of problems.