Local Stability Enhancement of Immersed Boundary Methods

The objective of this work is to develop a strategy to improve the robustness of immersed boundary methods. The basic approach was introduced for specific types of partial difierential equations in our previous publications. This paper elaborates on these ideas and provides a more general framework on how to apply the concept of local stability enhancement to difierent types of problems of engineering interest. The key feature of this immersed boundary method is that local stability constraints are taken into account in the derivation of thefinite-Difierence stencil coeficients at irregular grid points. Various applications of this immersed method are presented to incorporate high-order discretization andfiuid-structure-interaction problems, where numerical robustness is still a key issue. The variety of successful applications of this immersed boundary approach demonstrates the robustness andfiexibility of the method achieved through improved stability characteristics.