Abstract
The objective of the present work is to present and validate a pseudo-spectral numerical scheme based on a variational formulation for the solution of three-dimensional, time-dependent wall-bounded forced and natural convective flows. One of the novel aspects of this numerical scheme is the use of rescaled Legendre-Lagrangian interpolants to represent the velocity and temperature in one direction. These interpolants were obtained by dividing the Legendre Lagrangian interpolants of same order by the square root of the corresponding weight used for Gauss-Lobatto quadrature. Results from two specific problems are presented as part of the validation process: Rayleigh-Bénard convection and steady and unsteady channel flow driven by an external oscillating streamwise pressure gradient.
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