Reference Map Technique for Incompressible Fluid--Structure Interaction Problems

We present a fully Eulerian approach to simulate soft structures immersed in an incompressible fluid. The flow is simulated on a fixed grid using a second order projection method to solve the incompressible Navier--Stokes equations, and the fluid--structure interfaces are modeled using the level set method. By introducing a reference map variable to model finite-deformation constitutive relations in the structure on the same grid as the fluid, the interfacial coupling is highly simplified. This fully Eulerian approach provides a computationally efficient alternative to moving mesh approaches. Example simulations featuring many-body contacts and flexible swimmers will be presented.