DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Longfei Li, RPI

**Title: ***
A stable partitioned FSI algorithm for incompressible flow and deforming beams
*

**Abstract:**
A new added-mass partitioned (AMP) algorithm is described for solving fluid-structure interaction (FSI) problems coupling
incompressible flows with thin elastic structures undergoing finite deformations. The AMP scheme
is fully second-order accurate and stable, without sub-time-step iterations, even for very light
structures when added-mass effects are strong.
The fluid, governed by the incompressible Navier-Stokes equations, is solved in velocity-pressure form using
a fractional-step method; large deformations are treated with a mixed Eulerian-Lagrangian approach on deforming
composite grids. The motion of the thin structure is governed by a generalized
Euler-Bernoulli beam model, and these equations are solved in a Lagrangian frame using two
approaches, one based on finite differences and the other on finite elements. The key AMP interface
condition is a generalized Robin (mixed) condition on the fluid pressure. This condition, which is derived
at a continuous level, has no adjustable parameters and
is applied at the discrete level to couple the partitioned domain solvers.
A normal-mode stability analysis is performed for a linearized model problem involving a beam separating two fluid
domains, and it is shown that the AMP scheme is stable independent of the ratio of the mass of the
fluid to that of the structure. A traditional partitioned (TP) scheme using a Dirichlet-Neumann
coupling for the same model problem is shown to be unconditionally unstable if the added mass of the
fluid is too large. A series of benchmark problems of increasing complexity are considered to
illustrate the behavior of the AMP algorithm, and to compare the behavior with that of the TP
scheme. The results of all these benchmark problems verify the
stability and accuracy of the AMP scheme.

**Time:** Friday, March 25, 2016, 1:30-2:20 p.m.

**Place:** Exploratory Hall, Room 4106

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491