Development of high order fictitious domain methods for unstructured grids

• Applicant: Dr.-Ing. Sascha Eisenträger
• Subject Area: Applied Mechanics, Statics and Dynamics
• Term: from 2016 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 283837142

With the advent of fast high-resolution computed tomography (CT) scanners three-dimensional information of the micro-structure is readily available. Using this data a fully automated numerical method for structural simulations is developed. Therefore, it is possible to assess the influence of a heterogeneous micro-structure on the global behavior of the component without any user intervention. The chosen approach is based on the fictitious domain concept and especially on the finite cell method (FCM) or the spectral cell method (SCM) as recently proposed by the author.The focus of the current research proposal is on the extension of the FCM and the SCM to unstructured grids. In this context, it is generally known that arbitrary geometries can be discretized by tetrahedral elements and that powerful mesh generators are available for this element type. Therefore, the first step is to develop a novel formulation of the FCM and the SCM based on tetrahedral grids. In the future also prismatic, pyramidal and polyhedral elements are included in this framework. To retain high rates of convergence as encountered in the p-FEM different high order nodal and hierarchical shape functions are implemented and tested. After developing a sound theoretical basis for the proposed approach it is evaluated in detail. Open questions including the influence of the size of the cells with respect to a typical length scale of the micro-structure and suitable time integration methods are investigated. Depending on the size of the micro-structural details a local mesh refinement might be needed to resolve the solution field. Regarding dynamical analyses, time integration schemes are responsible for the accuracy of the solution and its efficiency. Therefore, it is inevitable to test different methods in view of their suitability for high order fictitious domain methods.Finally, the proposed method is validated using two different engineering problems. The first area of application is the mechanical assessment of cast components. The second application deals with the analysis of materials used for encapsulations of engines. In both cases the numerical model is based on CT scans of the real part. Depending on the micro-structure of the used materials a local meh refinement of the tetrahedral cells might be required. The analysis of these complex practice-oriented problems demonstrates the performance of the method and its applicability to complex industrial problems.

• DFG Programme: Research Grants