Chebyshev spectral and pseudospectral solutions of the Navier-Stokes equations
This paper presents numerical solutions obtained by Chebyshev approximations of thermal convection flows. In the first part, a Chebyshev Tau method with influence matrix technique for the pressure computation is applied to the simulation of convective phenomena in liquid metals. Some results are compared with those produced by finite elements. In the second part, a pseudospectral algorithm using finite element preconditioning for the momentum equations and finite difference preconditioning for the temperature equation treats thermal convection in a fluid whose viscosity is strongly temperature dependent. As finite element-pseudospectral schemes (FE-PS) are recent, some test problems are solved to assess their performance.
KeywordsRayleigh Number Thermal Convection Spectral Space Spectral Accuracy Chebyshev Space
Unable to display preview. Download preview PDF.
- G. De Vahl Davis, Report 1982/FMT/2, School of Mech. and Ind. Eng.,1982.Google Scholar
- M. Deville, Recent developments of spectral and pseudospectral methods in fluid dynamics, V.K.I course, 1984.Google Scholar
- M. Deville, E. Mund, Chebyshev pseudospectral solution of second order elliptic equation with finite element preconditioning, subm.to J.C.P., 1984.Google Scholar
- D. Gottlieb, S. Orszag, Siam monograph n°26, SIAM, Philadelphia 1977.Google Scholar
- P. Haldenwang, G. Labrosse, S. Abboudi, M. Deville, J. Comp. Phys., vol. 54, 1984.Google Scholar
- L. Kleiser, U. Schumann, Proc.3rd GAMM conf. on Num.Meth. in fluid Mech., p. 165–173, 1980.Google Scholar
- P. Le Queré, T. Alziary de Roquefort, C.R. Acad.Sc.Paris, t.294, série IIp.941–944, 1982.Google Scholar