Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems
This paper presents the application of adaptive rational spectral methods to the linear stability analysis of nonlinear fourth-order problems. Our model equation is a phase-field model of infiltration, but the proposed discretization can be directly extended to similar equations arising in thin film...
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| Format: | Article |
| Language: | en_US |
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Elsevier
2010
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| Online Access: | http://hdl.handle.net/1721.1/59995 https://orcid.org/0000-0002-7370-2332 https://orcid.org/0000-0003-3958-7382 |
| _version_ | 1826203605258993664 |
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| author | Cueto-Felgueroso, Luis Juanes, Ruben |
| author2 | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering Cueto-Felgueroso, Luis Juanes, Ruben |
| author_sort | Cueto-Felgueroso, Luis |
| collection | MIT |
| description | This paper presents the application of adaptive rational spectral methods to the linear stability analysis of nonlinear fourth-order problems. Our model equation is a phase-field model of infiltration, but the proposed discretization can be directly extended to similar equations arising in thin film flows. The sharpness and structure of the wetting front preclude the use of the standard Chebyshev pseudo-spectral method, due to its slow convergence in problems where the solution has steep internal layers. We discuss the effectiveness and conditioning of the proposed discretization, and show that it allows the computation of accurate traveling waves and eigenvalues for small values of the initial water saturation/film precursor, several orders of magnitude smaller than the values considered previously in analogous stability analyses of thin film flows, using just a few hundred grid points. |
| first_indexed | 2024-09-23T12:39:55Z |
| format | Article |
| id | mit-1721.1/59995 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:39:55Z |
| publishDate | 2010 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | mit-1721.1/599952022-10-01T10:23:37Z Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems Cueto-Felgueroso, Luis Juanes, Ruben Massachusetts Institute of Technology. Department of Civil and Environmental Engineering Juanes, Ruben Juanes, Ruben Cueto-Felgueroso, Luis This paper presents the application of adaptive rational spectral methods to the linear stability analysis of nonlinear fourth-order problems. Our model equation is a phase-field model of infiltration, but the proposed discretization can be directly extended to similar equations arising in thin film flows. The sharpness and structure of the wetting front preclude the use of the standard Chebyshev pseudo-spectral method, due to its slow convergence in problems where the solution has steep internal layers. We discuss the effectiveness and conditioning of the proposed discretization, and show that it allows the computation of accurate traveling waves and eigenvalues for small values of the initial water saturation/film precursor, several orders of magnitude smaller than the values considered previously in analogous stability analyses of thin film flows, using just a few hundred grid points. Massachusetts Institute of Technology. Computation for Design and Optimization Program Eni S.p.A. (Firm) 2010-11-17T15:57:35Z 2010-11-17T15:57:35Z 2009-06 2009-05 Article http://purl.org/eprint/type/JournalArticle 0021-9991 http://hdl.handle.net/1721.1/59995 Cueto-Felgueroso, Luis, and Ruben Juanes. “Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems.” Journal of Computational Physics 228.17 (2009): 6536-6552. © 2009 Elsevier Inc. https://orcid.org/0000-0002-7370-2332 https://orcid.org/0000-0003-3958-7382 en_US http://dx.doi.org/10.1016/j.jcp.2009.05.045 Journal of Computational Physics Attribution-Noncommercial-Share Alike 3.0 Unported http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Elsevier MIT web domain |
| spellingShingle | Cueto-Felgueroso, Luis Juanes, Ruben Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems |
| title | Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems |
| title_full | Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems |
| title_fullStr | Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems |
| title_full_unstemmed | Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems |
| title_short | Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems |
| title_sort | adaptive rational spectral methods for the linear stability analysis of nonlinear fourth order problems |
| url | http://hdl.handle.net/1721.1/59995 https://orcid.org/0000-0002-7370-2332 https://orcid.org/0000-0003-3958-7382 |
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