Date of Award
Doctor of Philosophy (PhD)
Kurt K. Maute
Carlos A. Felippa
This thesis presents a space-time extended finite element method (space-time XFEM)
based on the Heaviside enrichment for transient problems with moving interfaces, and its applications to the fluid-structure interaction (FSI) analysis. The Heaviside-enriched XFEM is a promising method to discretize partial differential equations with discontinuities in space. However, significant approximation errors are introduced by time stepping schemes when the interface geometry changes in time. The proposed space-time XFEM applies the finite element discretization and the Heaviside enrichment in both space and time with elements forming a space-time slab. A simple space-time scheme is introduced to integrate the weak form of the governing equations. This scheme considers spatial intersection configuration at multiple temporal integration points. Standard spatial integration techniques can be applied for each spatial configuration. Nitsche's method and the face-oriented ghost-penalty method are extended to the proposed space-time XFEM formulation. The stability, accuracy and flexibility of the space-time XFEM for various interface conditions including moving interfaces are demonstrated with structural and fluid problems. Moreover, the space-time XFEM enables analyzing complex FSI problems using moving interfaces, such as FSI with contact. Two FSI methods using moving interfaces (full-Eulerian FSI and Lagrangian-immersed FSI) are studied. The Lagrangian-immersed FSI method is a mixed formulation of Lagrangian and Eulerian descriptions. As solid and fluid meshes are independently defined, the FSI is computed between non-matching interfaces based on Nitsche's method and projection techniques adopted from computational contact mechanics. The stabilized Lagrange multiplier method is used for contact. Numerical examples of FSI and FSI-contact problems provide insight into the characteristics of the combination of the space-time XFEM and the Lagrangian-immersed FSI method. The proposed combination is a promising method which has the versatility for various multi-physics simulations and the applicability such as optimization.
Nagai, Toshiki, "Space-Time Extended Finite Element Method with Applications to Fluid-Structure Interaction Problems" (2018). Aerospace Engineering Sciences Graduate Theses & Dissertations. 198.