Local Stability Enhancement of Immersed Boundary/Interface Methods

The objective of this work is to present a novel, robust, high-order accurate Immersed Interface/Boundary Method (IIM ). In contrast to other immersed methods, which lack a posteriori check of the numerical stability, the method presented herein combines a local Taylor-series expansion at irregular grid points with a local stability condition as part of the design process. Furthermore, this work demonstrates that the local stability constraint is su cient to ensure a globally stable method as long as the DFL-number is less than its limiting value. To validate our novel approach, several test-cases from uid mechanics and electromagnetics are presented.