Interface handling for three‐dimensional higher‐order XFEM‐computations in fluid–structure interaction

Abstract

Three-dimensional higher-order eXtended finite element method (XFEM)-computations still pose challenging computational geometry problems especially for moving interfaces. This paper provides a method for the localization of a higher-order interface finite element (FE) mesh in an underlying three-dimensional higher-order FE mesh. Additionally, it demonstrates, how a subtetrahedralization of an intersected element can be obtained, which preserves the possibly curved interface and allows therefore exact numerical integration.The proposed interface algorithm collects initially a set of possibly intersecting elements by comparing their 'eXtended axis-aligned bounding boxes'. The intersection method is applied to a highly reduced number of intersection candidates. The resulting linearized interface is used as input for an elementwise constrained Delaunay tetrahedralization, which computes an appropriate subdivision for each intersected element. The curved interface is recovered from the linearized interface in the last step. The output comprises triangular integration cells representing the interface and tetrahedral integration cells for each intersected element.Application of the interface algorithm currently concentrates on fluid-structure interaction problems on low-order and higher-order FE meshes, which may be composed of any arbitrary element types such as hexahedra, tetrahedra, wedges, etc. Nevertheless, other XFEM-problems with explicitly given interfaces or discontinuities may be tackled in addition. Multiple structures and interfaces per intersected element can be handled without any additional difficulties. Several parallelization strategies exist depending on the desired domain decomposition approach. Numerical test cases including various geometrical exceptions demonstrate the accuracy, robustness and efficiency of the interface handling.

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

“…The principle idea of XFEM is shown in Figure 11, simplified for a crack in one dimension. Though XFEM has originally been developed for fracture, it has been extended to numerous applications including two-phase flow [122,123], fluid-structure interaction [124,125], biomechanics [126], inverse problems [127,128], multifield problems [129][130][131][132], among others. XFEM has been incorporated meanwhile into commercial software (XFEM) and has become one of the most popular methods for fracture.…”

An XFEM‐based embedding mesh technique for incompressible viscous flows

“…Thus, no global level-set functions or analytic functions are required. Subsequently, we apply a subdivision into tetrahedrons for domain integrals and triangles for boundary integrals [29] to accurately integrate the weak form in intersected elements. This integration cell technique is applicable to low-and high-order FEs and high-order interface approximations.…”

“…The interface is localized by the surface mesh of the embedded fluid patch. With the help of parallel search trees [29], first all intersected elements are determined. The relative position to the interface, which is required to evaluate the Heaviside function Equation (42), is obtained via the normal vector of the surface patch elements.…”

Finite element analysis on implicitly defined domains: An accurate representation based on arbitrary parametric surfaces

“…In our approach, we use linear sub-elements (finer mesh) incorporated into a boundary element E B to control a priori the faithfulness of the boundary representation. This approach was also used with boundaries represented by an analytical level set in 2D [40] and explicit 3D polygonal mesh in [43,44]. Following ideas similar to the Heaviside step function approach of [9,36], we will define the indicator functions K I[B and N B to simplify the description of the domain X h and its boundary C h , respectively, as follows:…”

“…Explicit surface representations independent of the mesh for 3D crack growth with hp-GFEM and interfaces in fluid-structure interaction with higher-order XFEM have been presented in the works of Pereira et al [43] and Mayer et al [44], respectively.…”