A unified continuum and variational multiscale formulation for fluids, solids, and fluid-structure interaction

Computational fluid-structure interaction (FSI) still faces several fundamental challenges. For example, in the classical FSI formulation, it is impossible to handle incompressibility in the solid model. The monolithic coupling approach, although more robust than the staggered approach, is still not well-accepted because it is complicated to implement and to solve.

In this talk, I will present a unified continuum modeling framework for viscous fluids and hyperelastic solids using the Gibbs free energy as the thermodynamic potential. Then we perform variational multiscale (VMS) analysis for this continuum body, which recovers the residual-based VMS formulation for the Navier-Stokes equations and provides a mechanism to circumvent the inf-sup condition for discretizing the solid problem. After that, I will discuss a novel unified formulation for fluid-solid coupled problems, which enjoys several appealing properties. The temporal scheme is more robust and more accurate in all Fourier modes. One can design an efficient and robust iterative solution method by using the algebraic multigrid method. More importantly, the new FSI formulation is straightforward to implement based on an existing CFD code. The connection between FSI and multiphase flow problems will be discussed.