zbMATH — the first resource for mathematics

A semi-implicit collocation method: Application to thermal convection in 2D compressible fluids. (English) Zbl 0724.76069
Summary: A semi-implicit pseudo-spectral collocation method using a third-order Runge-Kutta numerical scheme for the full Navier-Stokes equations is described. The Courant-Friedrichs-Lewy condition is overcome by the implicit handling of a diffusive term, as suggested by D. S. Harned and W. Kerner [J. Comput. Phys. 60, 62-75 (1985; Zbl 0581.76057)]. All such terms are solved with an iterative scheme in the Fourier space. Simulation of thermal convection in 2D comressible fluids is made by expanding variables on a Fourier-Chebyshev basis. We give some examples of sub- and supersonic steady solutions in the case where the heat flux at the upper boundary is governed by a black body.

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76R10 Free convection
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
Full Text: DOI
[1] , and , Spectral Methods in Fluid Dynamics, Springer, New York, 1988. · Zbl 0658.76001
[2] and , ’Spectral methods for CFD’, ICASE Report No. 89-13, 1989.
[3] Passot, J. Comput. Phys. 75 pp 300– (1988)
[4] and , Appl. Numer. Math., in the press.
[5] and , ’Three-dimensional gas dynamics in a sphere’, Preprint, Observatoire de Meudon, 1988.
[6] and , ’Direct simulation of viscous compressible transitional flows’, ONERA Report No. 1987-23, 1987.
[7] Gauthier, J. Comput. Phys. 75 pp 217– (1988)
[8] Graham, J. Fluid Mech. 70 pp 689– (1975)
[9] Hurlburt, Astrophys. J. 282 pp 557– (1984)
[10] Chan, Astrophys. J. 263 pp 935– (1982)
[11] Yamaguchi, Publ. Astron. Soc. Japan 37 pp 735– (1985)
[12] Publ. Astron. Soc. Japan 36 pp 613– (1984)
[13] , and , ’Simulations of unstable fluid flow using the piecewise-parabolic-method (PPM)’, Preprint, 1987.
[14] and , Numerical Analysis of Spectral Methods: Theory and Applications, CBMS-NSF Regional Conferences Series in Applied Mathematics, SIAM, Philadelphia, 1977.
[15] Harned, J. Comput. Phys. 60 pp 62– (1985)
[16] Williamson, J. Comput. Phys. 35 pp 48– (1980)
[17] and , Fluid Mechanics, Pergamon, Oxford, 1959.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.