Speaker
Description
The Immersed Boundary (IB) method is widely used for problems that involve fluid-structure interactions or complex geometries. However, when adapted to flows with rigid objects, the IB method typically involves either using penalty forces, which only approximately satisfy boundary conditions, or they are formulated as constraint problems that suffer from the need to solve a linear system that is poorly conditioned. These types of fluid-structure interactions are important for many biological applications, including swimming organisms and flows with rigid particles. Here, we present the Immersed Boundary Double Layer (IBDL) method for boundary value problems. It relies on a reformulation of the IB method that corresponds to a regularized second-kind integral equation. The linear solve is then well-conditioned and can therefore be accomplished with a small number of iterations of a Krylov method without preconditioning. Therefore, this method is highly beneficial for time-dependent problems for which this solve is done at every time step. We present the method formulation and recent developments.
