Spline-based methods for aerothermoelastic problems

  • Spline-basierte Methoden für aerothermoelastische Probleme

Make, Michael Karl Petronella; Behr, Marek (Thesis advisor); Elgeti, Stefanie Nicole (Thesis advisor)

Aachen : RWTH Aachen University (2021)
Dissertation / PhD Thesis

Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, 2021

Abstract

This thesis investigates the role of geometry representation in the numerical analysis of aerothermoelastic problems. Nowadays, numerical analysis on spline-based geometric objects is possible through isogeometric analysis (IGA) by utilizing the spline-basis for numerical analysis. Although IGA allows for the analysis of volumetric splines, generating such splines is not trivial. For the analysis of thin-walled elastic structures, this drawback can be circumvented by applying shell-theory. For most fluid problems, however, such a workaround does not exist. The NURBS-enhanced finite element method (NEFEM) solves this issue by requiring only the domain boundaries to be defined using splines. Both the NEFEM and IGAprovide an exact geometric boundary representation for numerical analysis. In the current work, NEFEM and IGA are coupled to provide a spline-based coupling interface in the context of fluid-structure interaction (FSI). The coupling is done within a strongly coupled partitioned solver framework, which allows for Dirichlet-Neumann (DN) and Robin-Neumann (RN) coupling. Combining NEFEM and IGA leads to a geometrically compatible fluid-structure interface defined by a single common spline. This enables a consistent and conservative transfer of coupling data between the fluid and structural domains. Furthermore, the common spline interface enables the direct integration of coupling quantities on the fluid and structural domains using the spline-basis. The numerical performance of the spline-based solver framework is investigated through a set of example problems. For compressible and incompressible flow problems, not considering FSI, improved numerical accuracy is observed when the exact geometry is considered through the NEFEM. An extension of this investigation to FSI problems shows similar behavior. It is found that especially fully-enclosed Dirichlet-bounded problems can benefit from the accurate boundary representation provided by the proposed spline-based method. Furthermore, the given examples show that using a common spline-basis can improve the numerical stability of the employed spatial coupling procedures. This observation is especially relevant for thermal coupled problems, for which such instabilities could lead to the inability to obtain converged numerical solutions.

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