First-order system least squares (FOSLS) for coupled fluid-elastic problems

Mathematical models for the mechanical coupling between a moving fluid and an elastic solid are inherently nonlinear because the shape of the Eulerian fluid domain is not known a priori – it is at least partially determined by the displacement of the elastic solid. In this paper, a first-order system least squares finite element formulation is used to solve the nonlinear system of model equations using different iteration techniques, including an approach where the equations are fully coupled and two other approaches in which the equations are decoupled. The discrete linear system of equations is solved using an algebraic multigrid solver as a preconditioner for a conjugate gradient iteration. The numerical results show that the approach is optimal in the sense that computational cost is proportional to the degrees of freedom. The results also show that the choice of iteration method, from fully coupled to fully decoupled, does not significantly effect computational cost, but it does influence the error in the solution.