Numerical Approaches and Computational Results for Fluid Dynamics Problems with Immersed Elastic Structures

Boyce Griffith, New York University

The immersed boundary (IB) method is a general purpose technique for the simulation of fluid-structure interaction. Originally introduced to study the flow patterns around heart valves, the IB method has been successfully applied to many problems in biofluid dynamics, including wave propagation in the cochlea, platelet aggregation, and aquatic animal locomotion. Common to all of these applications is the necessity of large computing resources. For 3D problems, parallel computing is a necessity.

To better utilize modern distributed memory parallel computers, last summer we began an ongoing project to implement the IB method using SAMRAI, a software toolkit developed at Lawrence Livermore National Laboratory. SAMRAI (Structured Adaptive Mesh Refinement Application Infrastructure) is an object-oriented C++ software framework which provides a flexible platform for implementing multi-physics scientific computing applications.

This effort aims to develop efficient distributed memory software for use with the 3D heart model of Peskin and McQueen. With this software, we are also investigating the use of adaptive mesh refinement and implicit timestepping schemes (i.e. nonlinear solvers) with the IB method. In addition to describing our most recent results on these fronts, I will give a brief overview of the immersed boundary formulation of fluid-structure interaction problems and describe numerical schemes for solving the IB equations.

Abstract Author(s): Boyce Griffith and Charles Peskin<br />(Courant Institute of Mathematical Sciences, New York University)<br />&nbsp;<br />Richard Hornung<br />(Center for Applied Scientific Computing, Lawrence Livermore National Laboratory)