Modeling and simulation of fluid–structure interaction in physics and biology

Abstract

Fluid--structure interaction (FSI) occurs widely across physics and biology. In this thesis, I present four projects in which I investigate systems with elements of FSI analytically, via simplified models, and numerically, via computational methods. Two projects investigate submerged solid bodies; the other two concern flow through porous media. In each pair, one project treats solids as rigid, so dynamics are driven purely by fluid. The other considers soft solids, coupling fluid evolution to the solid mechanics of deformation. In Chapter 1, I investigate a simple model swimmer consisting of rigid spheres submerged in fluid with intermediate levels of inertia. I use asymptotic expansion to extract a set of coupled equations describing the steady flow. These equations are solved numerically and asymptotically. The results unify previous investigations of similar systems and show the effects of fluid inertia on such swimmers differ significantly than those of solid inertia. In Chapter 2, I share a co-developed method for the simulation of multiple soft submerged bodies in three dimensions. Solid stresses are calculated on an Eulerian mesh using the reference map technique (RMT), allowing for coupling to fluid simulation. The RMT also allows for defining active stresses via body-embedded reference coordinates. This is demonstrated by a cylindrical swimmer with wavelike swimming gait driven by in-plane active stresses. In Chapter 3, I present a model for flow-driven erosion of a rigid porous matrix, where a simple rule for erosion gives rise to branching patterns. Using scaling arguments, I show the model dynamics depend on the manner in which the erosion threshold evolves and the evolution of the forcing flow. I numerically time-integrate the system and show how the resulting pattern formation depends on system parameters. In Chapter 4, I share a high-performance method for simulating flow through incompressible, deforming porous media. The technique is inspired by Chorin projection methods, where a proposed (compressible) material velocity field is projected onto the space of incompressible vector fields. I describe the implementation and present performance tests in two and three dimensions across multiple cores. Finally, I use the method to describe active cytoskeletal gels subject to molecular motor binding dynamics.