Abstract
Classical semi-implicit backward Euler/Adams Bashforth time discretizations of the Navier -Stokes equations induce, for high-Reynolds number flows, severe restrictions on the time step. Such restrictions can be relaxed by using semi-Lagrangian schemes essentially based on splitting the full problem into an explicit transport step and an implicit diffusion step. In comparison with the standard characteristics method, the semi-Lagrangian method has the advantage of being much less CPU time consuming where spectral methods are concerned. This paper is devoted to the comparison of the semi-implicit' and 'semi-Lagrangian' approaches, in terms of stability, accuracy and computational efficiency. Numerical results on the advection equation, Burger's equation and finally two- and three-dimensional Navier-Stokes equations, using spectral elements or a collocation method, are provided
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