A discrete forcing method dedicated to moving bodies in two-phase flow

The numerical simulation of interaction between structures and two-phase flows is a major concern for many industrial applications. To address this challenge, the motion of structures has to be tracked accurately. In this work, a discrete forcing method based on a porous medium approach is proposed to follow a nondeformable rigid body with an imposed velocity by using a finite-volume Navier-Stokes solver code dedicated to multiphase flows and based on a two-fluid approach. To deal with the action reaction principle at the solid wall interfaces in a conservative way, a porosity is introduced allowing to locate the solid and insuring no diffusion of the fluid-structure interface. The volumetric fraction equilibrium is adapted to this novelty. Mass and momentum balance equations are formulated on a fixed Cartesian grid. Interface tracking is addressed in detail going from the definition of the porosity to the changes in the discretization of the momentum balance equation. This so-called time- and space-dependent porosity method is then validated by using analytical and elementary test cases.