A reduced unified continuum formulation for vascular fluid–structure interaction

We recently derived the unified continuum and variational multiscale formulation for fluid-structure interaction (FSI) using Gibbs free energy. Restricting our attention to vascular FSI, we now reduce this arbitrary Lagrangian-Eulerian (ALE) by adopting three assumptions wall. The resulting reduced achieves monolithic FSI coupling in Eulerian frame through a simple modification of fluid boundary integral. While ostensibly similar semi-discrete coupled momentum method, its underlying derivation does not rely on an assumption fictitious body force elastodynamics sub-problem therefore represents direct simplification ALE method. Uniform temporal discretization is performed via generalized-$\alpha$ scheme. In contrast predominant approach yielding only first-order accuracy pressure, collocate both pressure velocity at intermediate time step achieve uniform second-order accuracy. conjunction with quadratic tetrahedral elements, methodology offers higher-order spatial quantities clinical interest. Furthermore, without loss consistency, segregated predictor multi-corrector algorithm developed preserve same block structure as incompressible Navier-Stokes equations implicit solver's associated linear system. Block preconditioning monolithically system made possible first time. Compared alternative preconditioners, three-level nested preconditioner, which improves representation Schur complement, demonstrates robust performance over wide range physical parameters. present verification against Womersley's deformable wall theory additionally develop practical modeling techniques applications.