A parallel fully-coupled fluid-structure interaction simulation of a cerebral aneurysm

A parallel fully-coupled approach has been developed for the fluid-structure interaction problem in a cerebral artery with aneurysm. An Arbitrary Lagrangian-Eulerian formulation based on the side-centered unstructured finite volume method [2] is employed for the governing incompressible Navier-Stokes equations and the classical Galerkin finite element formulation is used to discretize the constitutive law for the Saint Venant- Kirchhoff material in a Lagrangian frame for the solid domain. A special attention is given to construct an algorithm with exact fluid mass/volume conservation while obeying the global discrete geometric conservation law (DGCL). The resulting large-scale algebraic linear equations are solved using a one-level restricted additive Schwarz preconditioner with a block-incomplete factorization within each partitioned sub-domains. The parallel implementation of the present fully coupled unstructured fluid-structure solver is based on the PETSc library for improving the efficiency of the parallel algorithm. The proposed numerical algorithm is applied to a complicated problem involving unsteady pulsatile blood flow in a cerebral artery with aneurysm as a realistic fluid-structure interaction problem encountered in biomechanics.