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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
MR Author ID:
163675
ORCID:
0000-0003-3769-0538
Email:
i.sloan@unsw.edu.au
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