High-order mesh curving by distortion minimization with boundary nodes free to slide on a 3D CAD representation
We propose a 3D mesh curving method that converts a straight-sided mesh to an optimal-quality curved high-order mesh that interpolates a CAD boundary representation. The main application of this method is the generation of discrete approximations of curved domains that are valid for simulation analy...
| Authors: | ; ; |
|---|---|
| Format: | Article |
| Publication date: | 2016 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/86072 |
| Online Access: | https://hdl.handle.net/2117/86072 https://dx.doi.org/10.1016/j.cad.2015.06.011 |
| Access Level: | Open access |
| Keyword: | 3D modeling Geometric analysis Curved high-order meshing Mesh smoothing Mesh untangling Mesh quality CAD interpolation Hierarchical minimization Models geomètrics Àrees temàtiques de la UPC::Enginyeria electrònica |
| _version_ | 1878733439244435456 |
|---|---|
| author | Ruiz-Gironés, Eloi |
| author2 | Roca, Xevi Sarrate, Jose |
| author2_role | author author |
| author_browse | Roca, Xevi Ruiz-Gironés, Eloi Sarrate, Jose |
| author_facet | Ruiz-Gironés, Eloi Roca, Xevi Sarrate, Jose |
| author_role | author |
| collection | UPCommons. Portal del coneixement obert de la UPC |
| description | We propose a 3D mesh curving method that converts a straight-sided mesh to an optimal-quality curved high-order mesh that interpolates a CAD boundary representation. The main application of this method is the generation of discrete approximations of curved domains that are valid for simulation analysis with unstructured high-order methods. We devise the method as follows. First, the boundary of a straight-sided high-order mesh is curved to match the curves and surfaces of a CAD model. Second, the method minimizes the volume mesh distortion with respect to the coordinates of the inner nodes and the parametric coordinates of the curve and surface nodes. The proposed minimization features untangling capabilities and therefore, it repairs the invalid elements that may arise from the initial curving step. Compared with other mesh curving methods, the only goal of the proposed residual system is to minimize the volume mesh distortion. Furthermore, it is less constrained since the boundary nodes are free to slide on the CAD curves and surfaces. Hence, the proposed method is well suited to generate curved high-order meshes of optimal quality from CAD models that contain thin parts or high-curvature entities. To illustrate these capabilities, we generate several curved high-order meshes from CAD models with the implementation detailed in this work. Specifically, we detail a node-by-node non-linear iterative solver that minimizes the proposed objective function in a block Gauss–Seidel manner. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_562c6df3f00a4bd8a2b08d2a654968f7 |
| institution | Universitat Politècnica de Catalunya (UPC) |
| instname_str | Universitat Politècnica de Catalunya (UPC) |
| language | eng |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:upcommons.upc.edu:2117/86072 |
| publishDate | 2016 |
| publishDateSort | 2016 |
| publisher | Elsevier |
| publisherStr | Elsevier |
| reponame_str | UPCommons. Portal del coneixement obert de la UPC |
| spelling | High-order mesh curving by distortion minimization with boundary nodes free to slide on a 3D CAD representation Ruiz-Gironés, Eloi Roca, Xevi Sarrate, Jose 3D modeling Geometric analysis Curved high-order meshing Mesh smoothing Mesh untangling Mesh quality CAD interpolation Hierarchical minimization Models geomètrics Àrees temàtiques de la UPC::Enginyeria electrònica We propose a 3D mesh curving method that converts a straight-sided mesh to an optimal-quality curved high-order mesh that interpolates a CAD boundary representation. The main application of this method is the generation of discrete approximations of curved domains that are valid for simulation analysis with unstructured high-order methods. We devise the method as follows. First, the boundary of a straight-sided high-order mesh is curved to match the curves and surfaces of a CAD model. Second, the method minimizes the volume mesh distortion with respect to the coordinates of the inner nodes and the parametric coordinates of the curve and surface nodes. The proposed minimization features untangling capabilities and therefore, it repairs the invalid elements that may arise from the initial curving step. Compared with other mesh curving methods, the only goal of the proposed residual system is to minimize the volume mesh distortion. Furthermore, it is less constrained since the boundary nodes are free to slide on the CAD curves and surfaces. Hence, the proposed method is well suited to generate curved high-order meshes of optimal quality from CAD models that contain thin parts or high-curvature entities. To illustrate these capabilities, we generate several curved high-order meshes from CAD models with the implementation detailed in this work. Specifically, we detail a node-by-node non-linear iterative solver that minimizes the proposed objective function in a block Gauss–Seidel manner. This research was partially supported by CONACYT-SENER (‘‘Fondo Sectorial CONACYT SENER HIDROCARBUROS’’, grant contract 163723) and by the Spanish Ministerio de Economía y Competitividad under grant CTM2014-55014-C3-3-R.The work of the second author was partially supported by the Boeing Co. and US Air Force Office of Scientific Research and European Commis- sion through the Boeing–MIT Alliance and Computational Math Program and Marie Skłodowska-Curie Actions (HiPerMeGaFlows project),respectively. Peer Reviewed Elsevier https://hdl.handle.net/2117/86072 https://dx.doi.org/10.1016/j.cad.2015.06.011 |
| spellingShingle | High-order mesh curving by distortion minimization with boundary nodes free to slide on a 3D CAD representation Ruiz-Gironés, Eloi 3D modeling Geometric analysis Curved high-order meshing Mesh smoothing Mesh untangling Mesh quality CAD interpolation Hierarchical minimization Models geomètrics Àrees temàtiques de la UPC::Enginyeria electrònica |
| title | High-order mesh curving by distortion minimization with boundary nodes free to slide on a 3D CAD representation |
| title_full | High-order mesh curving by distortion minimization with boundary nodes free to slide on a 3D CAD representation |
| title_fullStr | High-order mesh curving by distortion minimization with boundary nodes free to slide on a 3D CAD representation |
| title_full_unstemmed | High-order mesh curving by distortion minimization with boundary nodes free to slide on a 3D CAD representation |
| title_short | High-order mesh curving by distortion minimization with boundary nodes free to slide on a 3D CAD representation |
| title_sort | High-order mesh curving by distortion minimization with boundary nodes free to slide on a 3D CAD representation |
| topic | 3D modeling Geometric analysis Curved high-order meshing Mesh smoothing Mesh untangling Mesh quality CAD interpolation Hierarchical minimization Models geomètrics Àrees temàtiques de la UPC::Enginyeria electrònica |
| topic_facet | 3D modeling Geometric analysis Curved high-order meshing Mesh smoothing Mesh untangling Mesh quality CAD interpolation Hierarchical minimization Models geomètrics Àrees temàtiques de la UPC::Enginyeria electrònica |
| url | https://hdl.handle.net/2117/86072 https://dx.doi.org/10.1016/j.cad.2015.06.011 |