An iterative pressure-correction method for the unsteady incompressible Navier-Stokes Equation
Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2016.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2016
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| Online Access: | http://hdl.handle.net/1721.1/104554 |
| _version_ | 1811091634803179520 |
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| author | Aoussou, Jean Philippe |
| author2 | Pierre F.J. Lermusiaux. |
| author_facet | Pierre F.J. Lermusiaux. Aoussou, Jean Philippe |
| author_sort | Aoussou, Jean Philippe |
| collection | MIT |
| description | Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2016. |
| first_indexed | 2024-09-23T15:05:30Z |
| format | Thesis |
| id | mit-1721.1/104554 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T15:05:30Z |
| publishDate | 2016 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1045542019-04-11T08:51:38Z An iterative pressure-correction method for the unsteady incompressible Navier-Stokes Equation Aoussou, Jean Philippe Pierre F.J. Lermusiaux. Massachusetts Institute of Technology. Computation for Design and Optimization Program. Massachusetts Institute of Technology. Computation for Design and Optimization Program. Computation for Design and Optimization Program. Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2016. Cataloged from PDF version of thesis. Includes bibliographical references (pages 53-59). The pressure-correction projection method for the incompressible Navier-Stokes equation is approached as a preconditioned Richardson iterative method for the pressure- Schur complement equation. Typical pressure correction methods perform only one iteration and suffer from a splitting error that results in a spurious numerical boundary layer, and a limited order of convergence in time. We investigate the benefit of performing more than one iteration. We show that that not only performing more iterations attenuates the effects of the splitting error, but also that it can be more computationally efficient than reducing the time step, for the same level of accuracy. We also devise a stopping criterion that helps achieve a desired order of temporal convergence, and implement our method with multi-stage and multi-step time integration schemes. In order to further reduce the computational cost of our iterative method, we combine it with an Aitken acceleration scheme. Our theoretical results are validated and illustrated by numerical test cases for the Stokes and Navier-Stokes equations, using Implicit-Explicit Backwards Difference Formula and Runge-Kutta time integration solvers. The test cases comprises a now classical manufactured solution in the projection method literature and a modified version of a more recently proposed manufactured solution. by Jean Philippe Aoussou. S.M. 2016-09-30T19:35:20Z 2016-09-30T19:35:20Z 2016 2016 Thesis http://hdl.handle.net/1721.1/104554 958626185 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 59 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Computation for Design and Optimization Program. Aoussou, Jean Philippe An iterative pressure-correction method for the unsteady incompressible Navier-Stokes Equation |
| title | An iterative pressure-correction method for the unsteady incompressible Navier-Stokes Equation |
| title_full | An iterative pressure-correction method for the unsteady incompressible Navier-Stokes Equation |
| title_fullStr | An iterative pressure-correction method for the unsteady incompressible Navier-Stokes Equation |
| title_full_unstemmed | An iterative pressure-correction method for the unsteady incompressible Navier-Stokes Equation |
| title_short | An iterative pressure-correction method for the unsteady incompressible Navier-Stokes Equation |
| title_sort | iterative pressure correction method for the unsteady incompressible navier stokes equation |
| topic | Computation for Design and Optimization Program. |
| url | http://hdl.handle.net/1721.1/104554 |
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