Speaker
Description
The Immersed Boundary Method (IBM) is widely used in the simulation of systems involving fluid-structure interaction [1]. The ability to simulate problems involving complex, moving geometry using a simple, Eulerian grid has led to the use of the IBM for the study of many biomechanical and biophysical systems. However, the study of chemical systems often necessitates the ability to impose Neumann or Robin boundary conditions at irregular locations on the Eulerian grid. Here, we present a method for imposing Neumann and Robin boundary conditions within an IBM framework. The method leverages the single-layer formulation of boundary integral equations, and we therefore refer to it as the Immersed Boundary Single Layer (IBSL) method. It requires solving a larger, augmented linear system. However, this system is well-conditioned and can be solved with a small number of iterations of a standard Kylov method without preconditioning. We also present some convergence results, limitations, and use cases of our methodology.
Bibliography
[1] Charles S. Peskin. The immersed boundary method. Acta Numerica, 11:479–517, 2002.
