On the relative merits of interpolation schemes for the immersed boundary method: a case study with the heat equation
In this work, three implementation options for the ghost cell immersed boundary method are compared. These options are alternatives to a rather common implementation of the method that is susceptible to numerical instability in the calculation of the bilinear interpolation in some cases. The met...
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Sociedade Brasileira de Matemática Aplicada e Computacional
2024-02-01
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| Series: | Trends in Computational and Applied Mathematics |
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| Online Access: | https://tema.sbmac.emnuvens.com.br/tema/article/view/1833 |
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| author | Willian Carlos Lesinhovski N. L. Dias L. S. Freire A. C. F. S. Jesus |
| author_facet | Willian Carlos Lesinhovski N. L. Dias L. S. Freire A. C. F. S. Jesus |
| author_sort | Willian Carlos Lesinhovski |
| collection | DOAJ |
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In this work, three implementation options for the ghost cell immersed boundary method are compared. These options are alternatives to a rather common implementation of the method that is susceptible to numerical instability in the calculation of the bilinear interpolation in some cases. The method is implemented for a second-order spatial discretization of the heat equation in a non-rectangular domain and the errors for each option are analyzed in terms of the order of accuracy and the way they are distributed in the domain. The best option, which was the only one to maintain the second order of convergence of the discretization, is to consider non-symmetric extrapolation with bilinear interpolation, instead of using inverse distance weighted interpolation with symmetric or non-symmetric extrapolation.
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| format | Article |
| id | doaj-art-b314b8e08a644bb78870694c36ac954d |
| institution | Kabale University |
| issn | 2676-0029 |
| language | English |
| publishDate | 2024-02-01 |
| publisher | Sociedade Brasileira de Matemática Aplicada e Computacional |
| record_format | Article |
| series | Trends in Computational and Applied Mathematics |
| spelling | doaj-art-b314b8e08a644bb78870694c36ac954d2025-02-05T20:32:30ZengSociedade Brasileira de Matemática Aplicada e ComputacionalTrends in Computational and Applied Mathematics2676-00292024-02-0126110.5540/tcam.2025.026.e01833On the relative merits of interpolation schemes for the immersed boundary method: a case study with the heat equationWillian Carlos Lesinhovski0https://orcid.org/0000-0003-1402-5957N. L. Dias1https://orcid.org/0000-0002-9770-8595L. S. Freire2https://orcid.org/0000-0002-8992-3869A. C. F. S. Jesus3https://orcid.org/0000-0003-0968-4296Universidade Federal do ParanáUniversidade Federal do ParanáUniversidade de São PauloUniversidade de São Paulo In this work, three implementation options for the ghost cell immersed boundary method are compared. These options are alternatives to a rather common implementation of the method that is susceptible to numerical instability in the calculation of the bilinear interpolation in some cases. The method is implemented for a second-order spatial discretization of the heat equation in a non-rectangular domain and the errors for each option are analyzed in terms of the order of accuracy and the way they are distributed in the domain. The best option, which was the only one to maintain the second order of convergence of the discretization, is to consider non-symmetric extrapolation with bilinear interpolation, instead of using inverse distance weighted interpolation with symmetric or non-symmetric extrapolation. https://tema.sbmac.emnuvens.com.br/tema/article/view/1833Immersed boundary methodBilinear interpolationInverse distance weighted interpolationHeat equation |
| spellingShingle | Willian Carlos Lesinhovski N. L. Dias L. S. Freire A. C. F. S. Jesus On the relative merits of interpolation schemes for the immersed boundary method: a case study with the heat equation Trends in Computational and Applied Mathematics Immersed boundary method Bilinear interpolation Inverse distance weighted interpolation Heat equation |
| title | On the relative merits of interpolation schemes for the immersed boundary method: a case study with the heat equation |
| title_full | On the relative merits of interpolation schemes for the immersed boundary method: a case study with the heat equation |
| title_fullStr | On the relative merits of interpolation schemes for the immersed boundary method: a case study with the heat equation |
| title_full_unstemmed | On the relative merits of interpolation schemes for the immersed boundary method: a case study with the heat equation |
| title_short | On the relative merits of interpolation schemes for the immersed boundary method: a case study with the heat equation |
| title_sort | on the relative merits of interpolation schemes for the immersed boundary method a case study with the heat equation |
| topic | Immersed boundary method Bilinear interpolation Inverse distance weighted interpolation Heat equation |
| url | https://tema.sbmac.emnuvens.com.br/tema/article/view/1833 |
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