Modeling Multiphase Flow Within and Around Deformable Porous Materials: A Darcy‐Brinkman‐Biot Approach

Abstract

We present a new computational fluid dynamics approach for simulating two-phase flow in hybrid systems containing solid-free regions and deformable porous matrices. Our approach is based on the derivation of a unique set of volume-averaged partial differential equations that asymptotically approach the Navier-Stokes Volume-of-Fluid equations in solid-free regions and multiphase Biot Theory in porous regions. The resulting equations extend our recently developed Darcy-Brinkman-Biot framework to multiphase flow. Through careful consideration of interfacial dynamics (relative permeability and capillary effects) and extensive benchmarking, we show that the resulting model accurately captures the strong two-way coupling that is often exhibited between multiple fluids and deformable porous media. Thus, it can be used to represent flow-induced material deformation (swelling, compression) and failure (cracking, fracturing). The model's open-source numerical implementation, hybridBiotInterFoam, effectively marks the extension of computational fluid mechanics into modeling multiscale multiphase flow in deformable porous systems. The versatility of the solver is illustrated through applications related to material failure in poroelastic coastal barriers and surface deformation due to fluid injection in porovisco-plastic systems.