An Operator Splitting Approach to the Solution of Fluid-Structure Interaction Problems in Hemodynamics

We present a loosely coupled partitioned method for the numerical simulation of a class of fluid-structure interaction problems in hemodynamics. This method is based on a time discretization by an operator-splitting scheme of the Lie’s type. The structure is assumed to be thin and modeled by the Koiter shell or membrane equations, while the fluid is modeled by the 3D Navier-Stokes equations for an incompressible viscous fluid. The fluid and structure are coupled via a full two-way coupling taking place at the moving fluid-structure interface, thus giving rise to a nonlinear moving-boundary problem. The Lie splitting decouples the fluid and structure sub-problems and is designed in such a way that the resulting partitioned scheme is unconditionally stable, without the need for any sub-iterations at every time step. Unconditional stability of the scheme is discussed using energy estimates, and several numerical examples are presented, showing that the scheme is first-order accurate in time. Implementation simplicity, computational efficiency, modularity, and unconditional stability make this scheme particularly appealing for solving FSI in hemodynamics. Martina Bukač Department of Applied and Computational Mathematics and Statistics, University of Notre Dame,153 Hurley Hall, Notre Dame, IN 46556, e-mail: [email protected] Sunčica Čanić Department of Mathematics, University of Houston, 4800 Calhoun Rd., Houston TX 77025 e-mail: [email protected] Boris Muha Department of Mathematics, Faculty of Science, University of Zagreb, Bijenicka 30, 10000 Zagreb, Croatia e-mail: [email protected] Roland Glowinski Department of Mathematics, University of Houston, 4800 Calhoun Rd. Houston TX 77025 e-mail: [email protected]