Eulerian simulation of complex suspensions and biolocomotion in three dimensions

We present a numerical method specifically designed for simulating three-dimensional fluid-structure interaction (FSI) problems based on the reference map technique (RMT). The RMT is a fully Eulerian FSI numerical method that allows fluids and large-deformation elastic solids to be represented on a single fixed computational grid. This eliminates the need for meshing complex geometries typical in other FSI approaches and greatly simplifies the coupling between fluid and solids. We develop a three-dimensional implementation of the RMT, parallelized using the distributed memory paradigm, to simulate incompressible FSI with neo-Hookean solids. As part of our method, we develop a field extrapolation scheme that works efficiently in parallel. Through representative examples, we demonstrate the method's suitability in investigating many-body and active systems, as well as its accuracy and convergence. The examples include settling of a mixture of heavy and buoyant soft ellipsoids, lid-driven cavity flow containing a soft sphere, and swimmers actuated via active stress.

Automated summary

The numerical method presented is specifically designed for simulating three-dimensional fluid-structure interaction problems based on the reference map technique. It simplifies the meshing of complex geometries typical in FSI simulations and greatly simplifies the coupling between fluids and solids. Through parallelization and a field extrapolation scheme, the method demonstrates efficiency and accuracy in simulating incompressible FSI with neo-Hookean solids.