A Self-Adaptive Strategy for the Time Integration of Navier-Stokes Equations

An efficient self-adaptive strategy for the explicit time integration of Navier-Stokes equations is presented. Unlike the conventional explicit integration schemes, it is not based on a standard CFL condition. Instead, the eigenvalues of the dynamical system are analytically bounded and the linear s...

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Bibliographic Details
Published in:Numerical heat transfer. Part B, Fundamentals Fundamentals, 2011-08, Vol.60 (2), p.116-134
Main Authors: Trias, F. X., Lehmkuhl, O.
Format: Article
Language:English
Subjects:
Computational efficiency
Dynamical systems
Eigenvalues
Equacions de Navier-Stokes
Equacions diferencials i integrals
Equacions en derivades parcials
Fluid mechanics
Matemàtiques i estadística
Mathematical analysis
Mètodes numèrics
Navier-Stokes equations
Numerical solutions
Robustness
Strategy
Time integration
Àrees temàtiques de la UPC
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Summary:An efficient self-adaptive strategy for the explicit time integration of Navier-Stokes equations is presented. Unlike the conventional explicit integration schemes, it is not based on a standard CFL condition. Instead, the eigenvalues of the dynamical system are analytically bounded and the linear stability domain of the time-integration scheme is adapted in order to maximize the time step. The method works independently of the underlying spatial mesh; therefore, it can be easily integrated into structured or unstructured codes. The additional computational cost is minimal, and a significant increase of the time step is achieved without losing accuracy. The effectiveness and robustness of the method are demonstrated on both a Cartesian staggered and an unstructured collocated formulation. In practice, CPU cost reductions up to more than 4 with respect to the conventional approach have been measured.
ISSN:1040-7790
1521-0626
DOI:10.1080/10407790.2011.594398