A Comparsion of Two Adaptive Versions of the Immersed Boundary Method

Boyce Griffith, New York University

Friday, October 2nd, 4:00 p.m., Phillips 332

The immersed boundary (IB) method treats problems of fluid-structure interaction in which an elastic or visco-elastic structure is immersed in a viscous, incompressible fluid. In the IB approach to such problems, an Eulerian description is employed for the fluid and a Lagrangian description is employed for the structure. Coupling between the Lagrangian and Eulerian descriptions is mediated by integral transforms with Dirac delta function kernels.

Adaptive versions of the IB method enable the deployment of high spatial resolution only where it is most needed (e.g., in the vicinity of fluid-structure interfaces and vortices shed from such interfaces), and allow for relatively coarse resolution to be employed where it suffices.

  In this talk, I will describe a general approach to constructing an 

adaptive version of the IB method, and I will provide examples of applications, including applications in cardiac fluid dynamics, which have been facilitated by such adaptive methods.

I will also describe in more detail two different adaptive versions of the IB method, including a cell-centered scheme which relies upon an approximate-projection fluid solver, and a staggered-grid scheme which uses an incompressible Stokes solver preconditioned by an exact projection method. Empirical results will be presented which illustrate various properties of these two adaptive schemes in the context of a canonical two-dimensional test case, namely an elliptical membrane immersed in a viscous incompressible fluid.