A parallel solver framework for fully implicit monolithic fluid-structure interaction

Abstract

We propose a suite of strategies for the parallel solution of fully implicit monolithic fluid-structure interaction (FSI). The solver is based on a modeling approach that uses the velocity and pressure as the primitive variables, which offers a bridge between computational fluid dynamics (CFD) and computational structural dynamics. The spatiotemporal discretization leverages the variational multiscale formulation and the generalized-α method as a means of providing a robust discrete scheme. In particular, the time integration scheme does not suffer from the overshoot phenomenon and optimally dissipates high-frequency spurious modes in both subproblems of FSI. Based on the chosen fully implicit scheme, we systematically develop a combined suite of nonlinear and linear solver strategies. Invoking a block factorization of the Jacobian matrix, the Newton-Raphson procedure is reduced to solving two smaller linear systems in the multi-corrector stage. The first is of the elliptic type, indicating that the algebraic multigrid method serves as a well-suited option. The second exhibits a two-by-two block structure that is analogous to the system arising in CFD. Inspired by prior studies, the additive Schwarz domain decomposition method and the block-factorization-based preconditioners are invoked to address the linear problem. Since the number of unknowns matches in both subdomains, it is straightforward to balance loads when parallelizing the algorithm for distributed-memory architectures. We use two representative FSI benchmarks to demonstrate the robustness, efficiency, and scalability of the overall FSI solver framework. In particular, it is found that the developed FSI solver is comparable to the CFD solver in several aspects, including fixed-size and isogranular scalability as well as robustness.