Dissipative spatial discretization of a phase field model of multiphase multicomponent isothermal fluid flow

This work is devoted to the development of a dissipative spatial discretization of a phase field model describing the dynamics of a multicomponent multiphase isothermal viscous compressible fluid with a resolved interface and effects associated with it (surface tension, wetting). Mass densities of mixture components are used as order parameters. The total Helmholtz free energy incorporates wall free energy providing wetting effects. The model under consideration is preliminary regularized, which allows one to increase time step in explicit time-marching methods. A finite-difference semi-discrete method is proposed and a discrete counterpart of the dissipativity theorem is proven. All the statements remain valid in the absence of regularization as well. 3D simulations of two-phase two-component and three-phase three-component fluids using explicit Euler method are performed. The simulation results confirm theoretical predictions.