Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems
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Author(s)
Cueto-Felgueroso, Luis
Juanes, Ruben
Date Issued
June 2009
Journal
Journal of Computational Physics
Publisher
Elsevier
Citation
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.
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Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
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Attribution-Noncommercial-Share Alike 3.0 Unported
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DOI of Published Version
https://doi.org/10.1016/j.jcp.2009.05.045
