Applied Mathematics Colloquium

Abstract:  Mathematical modeling and numerical simulations have been recognized as important tools for understanding human cardiovascular physiology and pathophysiology. We will discuss mathematical and computational models for the fluid-structure interaction (FSI) between blood flow and arterial walls. We describe the fluid flow by the Navier-Stokes equations for an incompressible viscous fluid, and we consider three cases for the structure problem: thin structure, composite structure, and poroelastic structure. The fluid and structure equations are coupled via the kinematic and dynamic coupling conditions, resulting in a nonlinear, moving boundary, FSI problem. To solve the problem numerically, we propose a partitioned numerical algorithm which is easily applied to the three different cases. We will present stability and convergence results, supported by numerical examples.

Room:  Mathematics/Psychology 104