Lightning Solvers for Potential Flows
We present a method for computing potential flows in planar domains. Our approach is based on a new class of techniques, known as “lightning solvers”, which exploit rational function approximation theory in order to achieve excellent convergence rates. The method is particularly suitable for flows i...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/5/4/227 |
| _version_ | 1797546234608615424 |
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| author | Peter J. Baddoo |
| author_facet | Peter J. Baddoo |
| author_sort | Peter J. Baddoo |
| collection | DOAJ |
| description | We present a method for computing potential flows in planar domains. Our approach is based on a new class of techniques, known as “lightning solvers”, which exploit rational function approximation theory in order to achieve excellent convergence rates. The method is particularly suitable for flows in domains with corners where traditional numerical methods fail. We outline the mathematical basis for the method and establish the connection with potential flow theory. In particular, we apply the new solver to a range of classical problems including steady potential flows, vortex dynamics, and free-streamline flows. The solution method is extremely rapid and usually takes just a fraction of a second to converge to a high degree of accuracy. Numerical evaluations of the solutions are performed in a matter of microseconds and can be compressed further with novel algorithms. |
| first_indexed | 2024-03-10T14:27:13Z |
| format | Article |
| id | doaj.art-78bdf350d2734ccc84cbb233a7228007 |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-10T14:27:13Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-78bdf350d2734ccc84cbb233a72280072023-11-20T22:55:04ZengMDPI AGFluids2311-55212020-11-015422710.3390/fluids5040227Lightning Solvers for Potential FlowsPeter J. Baddoo0Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UKWe present a method for computing potential flows in planar domains. Our approach is based on a new class of techniques, known as “lightning solvers”, which exploit rational function approximation theory in order to achieve excellent convergence rates. The method is particularly suitable for flows in domains with corners where traditional numerical methods fail. We outline the mathematical basis for the method and establish the connection with potential flow theory. In particular, we apply the new solver to a range of classical problems including steady potential flows, vortex dynamics, and free-streamline flows. The solution method is extremely rapid and usually takes just a fraction of a second to converge to a high degree of accuracy. Numerical evaluations of the solutions are performed in a matter of microseconds and can be compressed further with novel algorithms.https://www.mdpi.com/2311-5521/5/4/227potential flowsvortex dynamicsfree streamlinesnumerical methods |
| spellingShingle | Peter J. Baddoo Lightning Solvers for Potential Flows Fluids potential flows vortex dynamics free streamlines numerical methods |
| title | Lightning Solvers for Potential Flows |
| title_full | Lightning Solvers for Potential Flows |
| title_fullStr | Lightning Solvers for Potential Flows |
| title_full_unstemmed | Lightning Solvers for Potential Flows |
| title_short | Lightning Solvers for Potential Flows |
| title_sort | lightning solvers for potential flows |
| topic | potential flows vortex dynamics free streamlines numerical methods |
| url | https://www.mdpi.com/2311-5521/5/4/227 |
| work_keys_str_mv | AT peterjbaddoo lightningsolversforpotentialflows |