Fixed-grid methods for moving interface problems offer a number of attractive properties and have therefore gained quite some popularity in recent time. In [9], we introduced a fixed-grid method based on eXtended Finite Element Method (XFEM) and Lagrange Multiplier (LM) techniques. This paper reviews the original method and its enhancements towards realistic problems. Major challenges are the proper resolution of flow features near the fluid-structure interface for which two enhancements are discussed: a straightforward approach based on local adaptivity and a hybrid method that combines ideas from fixed-grid methods and Arbitrary Lagrangean Eulerian formulations. Furthermore, necessary steps to extend this XFEM/LM towards three-dimensional applications will be sketched.     «

Fixed-grid methods for moving interface problems offer a number of attractive properties and have therefore gained quite some popularity in recent time. In [9], we introduced a fixed-grid method based on eXtended Finite Element Method (XFEM) and Lagrange Multiplier (LM) techniques. This paper reviews the original method and its enhancements towards realistic problems. Major challenges are the proper resolution of flow features near the fluid-structure interface for which two enhancements are dis...     »