Daniel Baumgärtner

A robust algorithm for implicit description of immersed geometries within a background mesh

The paper presents a robust algorithm, which allows to implicitly describe and track immersed geometries within a background mesh. The background mesh is assumed to be unstructured and discretized by tetrahedrons. The contained geometry is assumed to be given as triangulated surface. Within the background mesh, the immersed geometry is described implicitly using a discontinuous distance function based on a level-set approach. This distance function allows to consider both, “double-sided” geometries like membrane or shell structures, and “single-sided” objects for which an enclosed volume is univocally defined. For the second case, the discontinuous distance function is complemented by a continuous signed distance function, whereas ray casting is applied to identify the closed volume regions. Furthermore, adaptive mesh refinement is employed to provide the necessary resolution of the background mesh. The proposed algorithm can handle arbitrarily complicated geometries, possibly containing modeling errors (i.e., gaps, overlaps or a non-unique orientation of surface normals). Another important advantage of the algorithm is the embarrassingly parallel nature of its operations. This characteristic allows for a straightforward parallelization using MPI. All developments were implemented within the open source framework “KratosMultiphysics” and are available under the BSD license. The capabilities of the implementation are demonstrated with various application examples involving practice-oriented geometries. The results finally show, that the algorithm is able to describe most complicated geometries within a background mesh, whereas the approximation quality may be directly controlled by mesh refinement.

Contribution to the Fluid-Structure Interaction Analysis of Ultra-Lightweight Structures using an Embedded Approach

Designing large ultra-lightweight structures within a fluid flow, such as inflatable hangars in an atmospheric environment, requires an analysis of the naturally occurring fluid-structure interaction (FSI). To this end multidisciplinary simulation techniques may be used. The latter, though, have to be capable of dealing with complex shapes and large deformations as well as challenging phenomena like wrinkling or folding of the structure. To overcome such problems the method of embedded domains may be used. In this work we discuss a new solution procedure for FSI analyses based on the method of embedded domains. In doing so, we are in particular answering the questions: How to track the interface in the embedded approach, how does the subsequent solution procedure look like and how does both compare to the well-known Arbitrary-Lagrangian-Eulerian (ALE) approach? In this context a level set technique as well as different mapping and mesh-updating strategies are developed and evaluated. Furthermore the solution procedure of a completely embedded FSI analysis is established and tested using different small- and large-scale examples. All results are finally compared to results from an ALE approach. It is shown that the embedded approach offers a powerful and robust alternative in terms of the FSI analysis of ultra-lightweight structures with complex shapes and large deformations. With regard to the solution accuracy, however, clear restrictions are elaborated.