Interactions between solids and fluids underpin the life and locomotion of living systems, yet many scientific puzzles remain unsolved about this seemingly simple mechanism. Efficient and accurate simulations have become mainstream tools to complement experiments when studying biophysical systems, e.g. in intracellular flow, red blood cells, and cardiovascular dynamics. However, developing fluid–structure interaction (FSI) methods is nontrivial. The key challenge is the intrinsic dichotomy in the preferred framework: Since solid stress comes from strain, solid simulations prefer Lagrangian methods; while fluid simulations favor Eulerian methods because fluid stress comes from strain rate.

State-of-the-art FSI methods can be broadly categorized into four types: mesh-free, Lagrangian, Eulerian–Lagrangian, and Eulerian. My research focuses on Eulerian methods, which avoid the extra computational cost of remeshing solids or managing communication between Lagrangian and Eulerian frameworks. Stress and velocity fields can be computed directly on the fixed grid, also simplifying multi-body contact. The basis of an Eulerian FSI method is representing solids within the Eulerian framework. One approach is the reference map technique (RMT), which uses a reference map field—an Eulerian mapping from the deformed state to the undeformed state of the solid—to model finite-strain large solid deformation in the Eulerian framework. The RMT can be coupled with any Eulerian numerical method for the fluid update.

In this work, I extended the reference map technique to the lattice Boltzmann (LB) method. The LB method has gained significant attention in the computational physics community for its simple and parallel fashion in simulating fluids. However, devising a fully-integrated LB method for modeling finite-strain solids poses the challenge of using the same fixed Eulerian grid and adhering to standard LB routines. With Prof. Chris Rycroft (UW–Madison), I developed the lattice Boltzmann reference map technique (LBRMT) to address these numerical challenges. A key feature of the LBRMT is a novel boundary condition that handles density differences across the solid–fluid interface. Our method successfully simulates hundreds of solids settling, rotating, and mixing with modest computational resources, offering a powerful tool for domain scientists to compare with experimental results. For instance, we investigated how the softness of solids (shear modulus) enhances the mixing rate for many soft bodies in a closed fluid system. While experiments or theoretical approaches alone cannot effectively track individual solids, our simulations enable us to do so. We discovered a scaling law that describes the relationship between shear modulus and mixing rate. Our in silico-driven approach can reveal theories applicable to real-world natural systems that may have previously seemed unattainable. This approach can be adapted to tackle specific challenges in areas such as soft condense matter, physics, and engineering.