High order solution of Poisson problems with piecewise constant coefficients and interface jumps
© 2017 Elsevier Inc. We present a fast and accurate algorithm to solve Poisson problems in complex geometries, using regular Cartesian grids. We consider a variety of configurations, including Poisson problems with interfaces across which the solution is discontinuous (of the type arising in multi-f...
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| Format: | Article |
| Language: | English |
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Elsevier BV
2021
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| Online Access: | https://hdl.handle.net/1721.1/134512 |
| _version_ | 1811076134516817920 |
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| author | Marques, Alexandre Noll Nave, Jean-Christophe Rosales, Rodolfo Ruben |
| author_facet | Marques, Alexandre Noll Nave, Jean-Christophe Rosales, Rodolfo Ruben |
| author_sort | Marques, Alexandre Noll |
| collection | MIT |
| description | © 2017 Elsevier Inc. We present a fast and accurate algorithm to solve Poisson problems in complex geometries, using regular Cartesian grids. We consider a variety of configurations, including Poisson problems with interfaces across which the solution is discontinuous (of the type arising in multi-fluid flows). The algorithm is based on a combination of the Correction Function Method (CFM) and Boundary Integral Methods (BIM). Interface and boundary conditions can be treated in a fast and accurate manner using boundary integral equations, and the associated BIM. Unfortunately, BIM can be costly when the solution is needed everywhere in a grid, e.g. fluid flow problems. We use the CFM to circumvent this issue. The solution from the BIM is used to rewrite the problem as a series of Poisson problems in rectangular domains—which requires the BIM solution at interfaces/boundaries only. These Poisson problems involve discontinuities at interfaces, of the type that the CFM can handle. Hence we use the CFM to solve them (to high order of accuracy) with finite differences and a Fast Fourier Transform based fast Poisson solver. We present 2-D examples of the algorithm applied to Poisson problems involving complex geometries, including cases in which the solution is discontinuous. We show that the algorithm produces solutions that converge with either 3rd or 4th order of accuracy, depending on the type of boundary condition and solution discontinuity. |
| first_indexed | 2024-09-23T10:16:45Z |
| format | Article |
| id | mit-1721.1/134512 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:16:45Z |
| publishDate | 2021 |
| publisher | Elsevier BV |
| record_format | dspace |
| spelling | mit-1721.1/1345122022-04-01T14:44:58Z High order solution of Poisson problems with piecewise constant coefficients and interface jumps Marques, Alexandre Noll Nave, Jean-Christophe Rosales, Rodolfo Ruben © 2017 Elsevier Inc. We present a fast and accurate algorithm to solve Poisson problems in complex geometries, using regular Cartesian grids. We consider a variety of configurations, including Poisson problems with interfaces across which the solution is discontinuous (of the type arising in multi-fluid flows). The algorithm is based on a combination of the Correction Function Method (CFM) and Boundary Integral Methods (BIM). Interface and boundary conditions can be treated in a fast and accurate manner using boundary integral equations, and the associated BIM. Unfortunately, BIM can be costly when the solution is needed everywhere in a grid, e.g. fluid flow problems. We use the CFM to circumvent this issue. The solution from the BIM is used to rewrite the problem as a series of Poisson problems in rectangular domains—which requires the BIM solution at interfaces/boundaries only. These Poisson problems involve discontinuities at interfaces, of the type that the CFM can handle. Hence we use the CFM to solve them (to high order of accuracy) with finite differences and a Fast Fourier Transform based fast Poisson solver. We present 2-D examples of the algorithm applied to Poisson problems involving complex geometries, including cases in which the solution is discontinuous. We show that the algorithm produces solutions that converge with either 3rd or 4th order of accuracy, depending on the type of boundary condition and solution discontinuity. 2021-10-27T20:05:20Z 2021-10-27T20:05:20Z 2017 2019-09-26T15:40:59Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/134512 Marques, Alexandre Noll, Jean-Christophe Nave, and Rodolfo Ruben Rosales. "High Order Solution of Poisson Problems with Piecewise Constant Coefficients and Interface Jumps." Journal of Computational Physics 335 (2017): 497-515. en 10.1016/J.JCP.2017.01.029 Journal of Computational Physics Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier BV arXiv |
| spellingShingle | Marques, Alexandre Noll Nave, Jean-Christophe Rosales, Rodolfo Ruben High order solution of Poisson problems with piecewise constant coefficients and interface jumps |
| title | High order solution of Poisson problems with piecewise constant coefficients and interface jumps |
| title_full | High order solution of Poisson problems with piecewise constant coefficients and interface jumps |
| title_fullStr | High order solution of Poisson problems with piecewise constant coefficients and interface jumps |
| title_full_unstemmed | High order solution of Poisson problems with piecewise constant coefficients and interface jumps |
| title_short | High order solution of Poisson problems with piecewise constant coefficients and interface jumps |
| title_sort | high order solution of poisson problems with piecewise constant coefficients and interface jumps |
| url | https://hdl.handle.net/1721.1/134512 |
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