Coupling Phase-Field LB–MP Method for Multiphase Fluid–Deformable Solid Interaction Problems Involving Large Density and Viscosity Contrasts

Abstract

A novel coupling phase-field lattice Boltzmann–material point (phase-field LB–MP) method is proposed in this work for multiphase fluid–solid bidirectional interaction problems. In this method, the phase-field lattice Boltzmann (LB) scheme is used to describe the multiphase incompressible fluid behaviors for its capability of dealing with binary-fluid system with large contrasts in both density and viscosity. The convected particle-domain interpolation-based material point method (MPM) is further adopted to capture the soft solid responses for its advantage in large deformation simulation and solid boundary representation. To bridge the solid and fluid phases, the Lagrangian marker points-based representation is proposed to explicitly depict the multiphase fluid–solid interface. Moreover, the hybrid bounce-back model is employed to effectively evaluate the unknown distribution functions and the contact angle specifying strategy for wetting boundary condition is developed for curved interface. The Galilean-invariant momentum exchange scheme and the distribution model are respectively taken into account to deal with hydrodynamic and capillary forces, and the interface-tracking force imposing strategy is developed for large deformation of solid. Additionally, the refilling algorithm is also considered for moving or deformable fluid–solid interface. There is no re-meshing operation needed for both fluid and solid parts in our phase-field LB–MP method. Three numerical examples are presented for progressively rigorous validations, which demonstrate that our phase-field LB–MP method has the capability of solving the multiphase fluid–deformable solid bidirectional interaction problems involving solid large deformation and binary-fluid behavior with large contrasts in both density and viscosity.