Numerical Simulation and Benchmarking of a Monolithic Multigrid Solver for Fluid-Structure Interaction Problems with Application to Hemodynamics

摘要: An Arbitrary Lagrangian-Eulerian (ALE) formulation is applied in a fully coupled monolithic way, considering the fluid-structure interaction (FSI) problem as one continuum. The mathematical description and numerical schemes are designed such way that general constitutive relations (which realistic for biomechanics applications) fluid well structural part can be easily incorporated. We utilize LBB-stable finite element pairs Q 2 P 1 + discretization space to gain high accuracy perform time-stepping 2nd order Crank-Nicholson, respectively, new modified Fractional-Step-θ-scheme both solid parts. resulting discretized nonlinear algebraic system solved by Newton method which approximates Jacobian matrices divided differences approach, linear systems direct or iterative solvers, preferably of Krylov-multigrid type.