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A pseudospectral quadrature method for Navier-Stokes equations on rotating spheres


Authors: M. Ganesh, Q. T. Le Gia and I. H. Sloan
Journal: Math. Comp. 80 (2011), 1397-1430
MSC (2010): Primary 65M12; Secondary 76D05
DOI: https://doi.org/10.1090/S0025-5718-2010-02440-8
Published electronically: November 29, 2010
MathSciNet review: 2785463
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Abstract: In this work, we describe, analyze, and implement a pseudospectral quadrature method for a global computer modeling of the incompressible surface Navier-Stokes equations on the rotating unit sphere. Our spectrally accurate numerical error analysis is based on the Gevrey regularity of the solutions of the Navier-Stokes equations on the sphere. The scheme is designed for convenient application of fast evaluation techniques such as the fast Fourier transform (FFT), and the implementation is based on a stable adaptive time discretization.


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Additional Information

M. Ganesh
Affiliation: Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado 80401
Email: mganesh@mines.edu

Q. T. Le Gia
Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
Email: qlegia@unsw.edu.au

I. H. Sloan
Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
Email: i.sloan@unsw.edu.au

DOI: https://doi.org/10.1090/S0025-5718-2010-02440-8
Keywords: Navier-Stokes equations, unit sphere, vector spherical harmonics
Received by editor(s): May 13, 2009
Received by editor(s) in revised form: April 18, 2010
Published electronically: November 29, 2010
Article copyright: © Copyright 2010 American Mathematical Society