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Evaluation and generic application scenarios for curved hexahedral adaptive mesh refinement

Elsweijer, Sandro (2022) Evaluation and generic application scenarios for curved hexahedral adaptive mesh refinement. Master's, Hochschule Bonn-Rhein-Sieg. doi: 10.13140/RG.2.2.34714.11203.

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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.

Item URL in elib:https://elib.dlr.de/186561/
Document Type:Thesis (Master's)
Title:Evaluation and generic application scenarios for curved hexahedral adaptive mesh refinement
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Elsweijer, SandroUNSPECIFIEDhttps://orcid.org/0000-0002-2753-3873UNSPECIFIED
Refereed publication:No
Open Access:Yes
Number of Pages:54
Keywords:adaptive mesh refinement, computational geometry, hexahedron, high-order meshes, mesh generation
Institution:Hochschule Bonn-Rhein-Sieg
Department:Fachbereich Elektrotechnik, Maschinenbau und Technikjournalismus
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space System Technology
DLR - Research area:Raumfahrt
DLR - Program:R SY - Space System Technology
DLR - Research theme (Project):R - Tasks SISTEC
Location: Köln-Porz
Institutes and Institutions:Institute for Software Technology > High-Performance Computing
Institute for Software Technology
Deposited By: Elsweijer, Sandro
Deposited On:09 Jun 2022 10:44
Last Modified:13 Jun 2022 13:03

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