Numerical Simulations of Liquid Drop Dynamics in Porous Medium Using Adaptive Mesh

The work deals with numerical simulations of multiphase flow and displacement front in porous media. In practice, the displaced fluid often forms compact inclusions surrounded by the displacing fluid. In this case, we should consider displacement fronts on both forward and back sides of the inclusion. The drop is initially spherical and the interface thickness between liquids is supposed to be small (much less than the drop radius). The calculations are carried out using the Darcy model by Level set method with adaptive mesh refinement algorithm that dynamically refines computational mesh near interface. The open source software PARAMESH is used to operate with the adaptive mesh. Numerical modelling of the droplet dynamics subjected to gravity has shown that the instability develops at the forefront of moving droplets regardless of the ratio of fluids viscosities. Under modulated pressure gradient small-scale perturbations of interface are suppressed and in the case of modulation with large enough intensity drop becomes stable.