Spectral Collocation Methods Dealing with Coordinate Singularities

Relevant Research:

Aidi Zhang, Philip S. Marcus (2024) Stable three-dimensional vortex families consistent with Jovian observations including the Great Red Spot, Journal of Fluid Mechanics 984, p. A61, url, doi:10.1017/jfm.2024.132

Sangjoon Lee, Philip S. Marcus (2024) Transient growth of a wake vortex and its initiation via inertial particles, arXiv preprint arXiv:2402.07469, url

Sangjoon Lee, Philip S. Marcus (2023) Linear stability analysis of wake vortices by a spectral method using mapped Legendre functions, Journal of Fluid Mechanics 967, p. A2, url, doi:10.1017/jfm.2023.455

Mani Mahdinia, Pedram Hassanzadeh, Philip S. Marcus, Chung-Hsiang Jiang (2017) Stability of three-dimensional Gaussian vortices in an unbounded, rotating, vertically stratified, Boussinesq flow: Linear analysis, Journal of Fluid Mechanics 824, p. 97-134, pdf, doi:10.1017/jfm.2017.303

Lawrence A. Sromovsky, Imke De Pater, Patrick M. Fry, Heidi B. Hammel, Philip S. Marcus (2015) High S/N Keck and Gemini AO imaging of Uranus during 2012–2014: New cloud patterns, increasing activity, and improved wind measurements, Icarus 258(1), p. 192-223, url, doi:10.1016/j.icarus.2015.05.029

Gregory J. McCauley, Philip S. Marcus, Ö. Savaş, Donald A. Durston (2006) Computational analysis of a passive wake alleviation scheme, Collection of Technical Papers - AIAA Applied Aerodynamics Conference 1, p. 30-53, pdf, doi:10.2514/6.2006-2820

Joseph A. Barranco, Philip S. Marcus (2006) A 3D spectral anelastic hydrodynamic code for shearing, stratified flows, Journal of Computational Physics 219(1), p. 21-46, pdf, doi:10.1016/j.jcp.2006.03.015

T. Matsushima, Philip S. Marcus (1997) A Spectral Method for Unbounded Domains, Journal of Computational Physics 137(2), p. 321-345, pdf, doi:10.1006/jcph.1997.5804

T. Matsushima, Philip S. Marcus (1995) A Spectral Method for Polar Coordinates, Journal of Computational Physics 120(2), p. 365-374, pdf, doi:10.1006/jcph.1995.1171

R. D. van Buskirk, Philip S. Marcus (1994) Spectrally Accurate Contour Dynamics, Journal of Computational Physics 115(2), p. 302-318, pdf, doi:10.1006/jcph.1994.1198

S. Bouaoudia, Philip S. Marcus (1991) Fast and accurate spectral treatment of coordinate singularities, Journal of Computational Physics 96(1), p. 217-223, pdf, doi:10.1016/0021-9991(91)90272-M

Philip S. Marcus (1986) Description and Philosophy of Spectral Methods, Astrophysical Radiation Hydrodynamics, Karl-Heiz A Winkler, Michael L Norman (ed.), p. 359-386, pdf, doi:10.1007/978-94-009-4754-2_10

Philip S. Marcus (1986) Numerical simulation of quasi-geostrophic flow using vortex and spectral methods, Numerical Analysis, eds. D. Griffiths and G. Watson, Pitman Research Note in Mathematics Series 140, p. 125-139


Sangjoon Lee, Philip S. Marcus (2021) Linear instability analysis of wake vortices by a spectral method using mapped Legendre functions, APS Division of Fluid Dynamics Meeting Abstracts, p. E24-001, url