Abstract
The computations are done using the Navier-Stokes equations within the vorticity-stream function formulation. These equations associated (in the case Pr=0.015) with the temperature equations are solved using the spectral method proposed in [1]. The time-differencing makes use of the semi-implicit Adams-Bashforth / second-order backward Euler scheme [1],[2]: the diffusive terms are considered implicitely while the nonlinear convective terms are evaluated explicitely. In this way, at each time step, we have to solve a Stokes-type problem for the vorticity and the streamfunction, and a Helmholtz equation for the temperature. The spatial approximation makes use of Chebyshev polynomial expansions in both directions. The boundary conditions in the Stokes-type problem are handled by means of an influence matrix technique, leading to the solution of Helmholtz equations only. These equations are solved by the Tau method associated with the matrix diagonalization technique leaving the major part of the calculations in a preprocessing stage.
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References
Vanel, J.M., Peyret, R., and Bontoux, P., A pseudo-spectral solution of vorticity-stream function equations using the influence matrix technique, in “Numerical methods for fluid dynamics II”, (K.W. Morton, M.J. Baines, Eds.), p. 463–475, Clarendon Press, Oxford,1986.
Ouazzani, J., Peyret, R. and Zakaria, A., Stability of collocation-Chebyshev schemes with application to the Navier-Stokes equations, Proc. Sixth GAMM Conf. on Numer. Meth. in Fluid Mechanics, Göttingen, 25–27 September, 1986, (D. Rues, W. Kordulla Eds), p. 287–294, Vieweg, Braunschweig, 1986.
Pulicani, J.P., Crespo, E., Bontoux, P., Randriamampianina, A., and Peyret, R., Spectral Simulations of Oscillatory Convection at Low Prandtl Number, Prépublication n°209, Laboratoire de Mathématiques, Université de Nice, Septembre 1988.
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© 1990 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig
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Pulicani, J.P., Peyret, R. (1990). Spectral Calculations of Convection in Low-Pr Fluids. In: Roux, B. (eds) Numerical Simulation of Oscillatory Convection on Low-Pr Fluids. Notes on Numerical Fluid Mechanics (NNFM), vol 27. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-87877-9_29
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DOI: https://doi.org/10.1007/978-3-322-87877-9_29
Publisher Name: Vieweg+Teubner Verlag
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