Newton Linearization of the Curvature Operator in Structured Grid Generation with Sample Solutions
Elliptic grid generation equations based on the Laplacian operator have the well-known property of clustering the mesh near convex boundaries and declustering it near concave boundaries. In prior work, a new differential operator was derived and presented to address this issue. This new operator ret...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2022/7266801 |
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| author | Pat Piperni Maahi M. Talukder |
| author_facet | Pat Piperni Maahi M. Talukder |
| author_sort | Pat Piperni |
| collection | DOAJ |
| description | Elliptic grid generation equations based on the Laplacian operator have the well-known property of clustering the mesh near convex boundaries and declustering it near concave boundaries. In prior work, a new differential operator was derived and presented to address this issue. This new operator retains the strong smoothing properties of the Laplacian without the latter’s adverse curvature effects. However, the new operator exhibits slower convergence properties than the Laplacian, which can lead to increased turnaround times and in some cases preclude the achievement of convergence to machine accuracy. In the work presented here, a Newton linearization of the new operator is presented, with the objective of achieving more robust convergence properties. Sample solutions are presented by evaluating a number of solvers and preconditioners and assessing the convergence properties of the solution process. The efficiency of each solution method is demonstrated with applications to two-dimensional airfoil meshes. |
| format | Article |
| id | doaj-art-b4ddf73c4fb44e0f81114bcb5f70e65a |
| institution | Kabale University |
| issn | 1687-0425 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b4ddf73c4fb44e0f81114bcb5f70e65a2025-02-03T06:12:25ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252022-01-01202210.1155/2022/7266801Newton Linearization of the Curvature Operator in Structured Grid Generation with Sample SolutionsPat Piperni0Maahi M. Talukder1Clarkson UniversityClarkson UniversityElliptic grid generation equations based on the Laplacian operator have the well-known property of clustering the mesh near convex boundaries and declustering it near concave boundaries. In prior work, a new differential operator was derived and presented to address this issue. This new operator retains the strong smoothing properties of the Laplacian without the latter’s adverse curvature effects. However, the new operator exhibits slower convergence properties than the Laplacian, which can lead to increased turnaround times and in some cases preclude the achievement of convergence to machine accuracy. In the work presented here, a Newton linearization of the new operator is presented, with the objective of achieving more robust convergence properties. Sample solutions are presented by evaluating a number of solvers and preconditioners and assessing the convergence properties of the solution process. The efficiency of each solution method is demonstrated with applications to two-dimensional airfoil meshes.http://dx.doi.org/10.1155/2022/7266801 |
| spellingShingle | Pat Piperni Maahi M. Talukder Newton Linearization of the Curvature Operator in Structured Grid Generation with Sample Solutions International Journal of Mathematics and Mathematical Sciences |
| title | Newton Linearization of the Curvature Operator in Structured Grid Generation with Sample Solutions |
| title_full | Newton Linearization of the Curvature Operator in Structured Grid Generation with Sample Solutions |
| title_fullStr | Newton Linearization of the Curvature Operator in Structured Grid Generation with Sample Solutions |
| title_full_unstemmed | Newton Linearization of the Curvature Operator in Structured Grid Generation with Sample Solutions |
| title_short | Newton Linearization of the Curvature Operator in Structured Grid Generation with Sample Solutions |
| title_sort | newton linearization of the curvature operator in structured grid generation with sample solutions |
| url | http://dx.doi.org/10.1155/2022/7266801 |
| work_keys_str_mv | AT patpiperni newtonlinearizationofthecurvatureoperatorinstructuredgridgenerationwithsamplesolutions AT maahimtalukder newtonlinearizationofthecurvatureoperatorinstructuredgridgenerationwithsamplesolutions |