The immersed interface method for flows around moving complex geometries

I will present the extension of the immersed interface method to simulate flows around moving complex geometries. The immersed interface method is a framework to solve differential equations with discontinuous solutions across interfaces. When it is employed to simulate a flow around a moving rigid object, the object is modeled as the fluid in the rigid motion enforced by singular force along the interface and body force inside the interface. The flow is then simulated by incorporating necessary jump conditions across the interface into discretization schemes on a fixed grid. In this talk, I will first describe how to implement the jump conditions in the immersed interface method. I will then present how to compute the jump conditions for objects with complex surfaces that are represented by triangular meshes. Lastly, I will show testing results to demonstrate the accuracy, efficiency and robustness of the method.