Modeling creeping flows in porous media using regularized Stokeslets

Flows in porous media in the low-Reynolds number regime are often modeled by the Brinkman equations. Analytical solutions to these equations are limited to standard geometries. Finite volume or element schemes can be used in more complicated geometries, but become cumbersome when there are moving boundaries that require frequent remeshing of the domain. In Newtonian fluids, the method of regularized Stokeslets has gained popularity due to its ease of implementation, including for moving boundaries, especially for swimming and pumping problems. While the corresponding method of regularized Brinkmanlets can be used in a domain consisting entirely of Brinkman medium, many applications would benefit from an easily implemented representation of flow in a domain with heterogeneous regions of Brinkman medium and Newtonian fluid. In this paper, we model flows in porous media by placing many static regularized Stokeslets randomly in three dimensions to emulate the forces exerted by the rigid porous structure. We perform numerical experiments to deduce the correspondence between the chosen density and blob size of regularized Stokeslets in our model, and a Brinkman medium. We demonstrate our model for two scenarios of microswimmers near porous media.