Combined Lattice Boltzmann and phase-field simulations for incompressible fluid flow in porous media

A Lattice-Boltzmann method for incompressible fluid flow is coupled with the dynamic equations of a phase-field model for multiple order parameters. The combined model approach is applied to computationally evaluate the permeability in porous media. At the boundaries between the solid and fluid phases of the porous microstructure, we employ a smooth formulation of a bounce-back condition related to the diffuse profile of the interfaces. We present simulations of fluid flow in both, static porous media with stationary non-moving interfaces and microstructures performing a dynamic evolution of the phase and grain boundaries. For the latter case, we demonstrate applications to dissolving grain structures with partial melt inclusions and computationally analyse the temporal evolution of the microporosity under wetting conditions at the melt-grain boundaries. In any development state of the material, the Darcy number and the hydraulic conductivity of the porous medium are evaluated for various types of fluid.