Fachbereich Elektrotechnik, Maschinenbau und Technikjournalismus
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Modern engineering relies heavily on utilizing computer technologies. This is especially true for thermoplastic manufacturing, such as blow molding. A crucial milestone for digitalization is the continuous integration of data in unified or interoperable systems. While new simulation technologies are constantly developed, data management standards such as STEP fail at integrating them. On the other hand, industrial standards such as ”VMAP” manage to improve interoperability for Small and Medium-sized Enterprises. However, they do not provide Simulation Process and Data Management (SPDM) technologies. For SPDM integration of VMAP data, Ontology-Based Data Access is used to allow continuing the digital thread in custom semantic-based open-source solutions. An ontology of the database format (VMAP) was generated alongside an expandable knowledge graph of data access methods. A Python-based software architecture was developed, automatically using the semantic representations of database format and data access to query data and metadata within the VMAP file. The result is a software architecture template that can be adapted for other data standards and integrated into semantic data management systems. It allows semantic queries on simulation data down to element-wise resolution without integrating the whole model information. The architecture can instantiate a file in a knowledge graph, query a file’s metadatum and, in case it is not yet available, find a semantically represented process that allows the creation and instantiation of the required metadatum. See Figure 1. The results of this thesis can be expected to form a basis for semantic SPDM tools.
In (dynamic) adaptive mesh refinement (AMR) an input mesh is refined or coarsened to the need of the numerical application. This refinement happens with no respect to the originally meshed domain and is therefore limited to the geometrical accuracy of the original input mesh. We presented a novel approach to equip this input mesh with additional geometry information, to allow refinement and high-order cells based on the geometry of the original domain. We already showed a limited implementation of this algorithm. Now we evaluate this prototype with a numerical application and we prove its influence on the accuracy of certain numerical results. To be as practical as possible, we implement the ability to import meshes generated by Gmsh and equip them with the needed geometry information. Furthermore, we improve the mapping algorithm, which maps the geometry information of the boundary of a cell into the cell's volume. With these preliminary steps done, we use out new approach in a simulation of the advection of a concentration along the boundary of a sphere shell and past the boundary of a rotating cylinder. We evaluate the accuracy of our approach in comparison to the conventional refinement of cells to answer our research question: How does the performance and accuracy of the hexahedral curved domain AMR algorithm compare to linear AMR when solving the advection equation with the linear finite volume method? To answer this question, we show the influence of curved AMR on our simulation results and see, that it is even able to outperform far finer linear meshes in terms of accuracy. We also see that the current implementation of this approach is too slow for practical usage. We can therefore prove the benefits of curved AMR in certain, geometry-related application scenarios and show possible improvements to make it more feasible and practical in the future.
In tree-based adaptive mesh refinement (AMR) we store refinement trees in the cells of an unstructured coarse mesh. This lets us combine the speed and simpler management of structured refinement trees with the more flexible mesh generation of the unstructured coarse mesh. But this creates a conflict between performance and geometrical accuracy. If we favor speed we reduce the cells in our coarse mesh and hence reduce the accuracy of our geometrical representation. If we want more accurate results we generate a finer coarse mesh and lose performance by managing more cells in our unstructured coarse mesh. To mitigate this conflict we present the prototype of an geometry description which we implement in an already existing library. With this description we build geometry adapted hexahedral refinement trees, which also support high-order curved boundary cells. We also present examples on how to use this description. Moreover, we test the speedup of this new algorithm compared with coarse meshes with different geometrical errors.