A three-phase interpenetrating continua approach for wave and porous structure interaction

A three phase interpenetrating continua model for the numerical simulation of water waves and porous structure interaction is proposed in this work. In contrast with one-fluid formulation/multi-component methods, each phase has its own characteristics, density, velocity, etc and each point is occupied by all phases, this model requires additional closure laws to describe the interfacial momentum exchange, e.g., via the Ergun's equation. First, the porous structure is modelled as a phase of continua with a penalty force adding on the momentum equation, so the conservation of mass is guaranteed without source terms. Second, the adaptive unstructured mesh modelling with P1DG-P1 elements is employed here to decrease the total number of degree of freedom maintaining the same order of accuracy. Several benchmark problems are used to validate the model, which includes the darcy flow, classical collapse of water column and water column with a porous structure.