A Computational Method for Simulating the Interaction between Fluid and Elastic Structures

Elijah Newren, University of Utah

Many biofluid problems involve the interaction of deformable, elastic structures with a surrounding fluid. While determining the fluid flow can be a difficult problem even without the presence of such structures, the addition of these structures adds a new dimension of difficulty. The Immersed Boundary (IB) method was originally designed for the simulation of flow patterns around heart valves, but it has been applied to diverse problems such as platelet aggregation, wave propagation in the cochlea, and aquatic animal locomotion. However, this method has some drawbacks. It suffers from lower order accuracy near the boundary, and for stiff problems it results in either a severe explicit timestep restriction or a large ill-conditioned implicit system. The Immersed Interface (II) method was introduced to address these limitations, but it poses new challenges. Extending the II method to three dimensions is nontrivial and has only been done in specialized cases. 

I will discuss these methods and how we are using Radial Basis Functions (RBFs) to extend a hybrid IB/II method to three dimensions. As these methods make necessary the use of parallel computing, I will be discussing the computational techniques and algorithms we are employing to solve this problem, such as multigrid, communication strategies with MPI, quasi-Newton methods, and our use of the SAMRAI package developed at Lawrence Livermore National Laboratory for efficient distributed memory communication and the ability to add adaptive mesh refinement in the future.

Abstract Author(s): Elijah Newren, Grady Wright, Aaron Fogelson