The diffuse interface approximation to fluid-structure interaction

We consider a fluid-structure interaction problem in the Eulerian, phase-field formulation. The problem is described using the Navier–Stokes equations for a viscous, incompressible fluid, coupled with the incompressible hyperelasticity system, both written in the Eulerian coordinates. This allows the problem to be written in a unified formulation, using a single field for the fluid and structure velocities. To track the position of the domain, we use a phase-field approach, resulting in a coupled Cahn–Hilliard–Navier–Stokes-type of problem for the diffuse interface fluid-structure interaction. Under certain assumptions, we prove the convergence of the diffuse interface model to the sharp interface fluid-structure interaction problem. To solve the problem numerically, we propose a novel, strongly coupled, second-order partitioned computational method where the system is decoupled into the Cahn–Hilliard problem, the transport problem for the left Cauchy–Green deformation tensor, and the Navier–Stokes problem. The problems are solved iteratively until convergence at each time step. The performance of the method is illustrated on two computational examples.