A Two-Way Coupled Fluid Structure Interaction Framework For Immersed Soft Porous Media

Flow and transport around immersed soft porous media are prevalent in biological systems. Examples include the perfusion of fluid within a bone scaffold matrix driven by mechanical deformation of the bone's porous structures. In the vascular system, the blockage and fracturing of porous blood clots under pulsatile flow are driven by clot-flow two-way interactions. These problems are characterized by a soft porous structure experiencing macro-scale deformation under viscous, flow-induced forces. Numerical simulations of the inherently multi-scale Fluid-Structure Interaction (FSI) of such porous structures are challenging. Mesh-conforming FSI methods are ill-suited for resolving FSI in porous media because the macro-scale deformation of the porous structure likely results in significant distortion of the pore-scale mesh elements. Non-conforming methods, such as the Immersed Finite Element Method (IFEM), provide an attractive avenue for simulating an immersed continuous structure without expensive re-meshing. However, a continuum-based representation of the porous structures does not effectively capture the inherently multi-scale nature of the problem. In this contribution, we extend traditional IFEM by representing the porous structure as a series of connected discrete elements. This discrete element representation enables the direct modeling of the structure’s porosity. The dynamics of the discrete element structure are solved using the Discrete Element Method (DEM), with fluid coupling modeled via IFEM on individual discrete elements. The resulting two-way coupled framework enables direct modeling of FSI around an immersed porous structure. To validate our implementation, we present results from a canonical immersed two-body problem simulated using our framework. Finally, we demonstrate an example application of our method by simulating the micromechanics of a porous blood clot under pulsatile flow.