On the efficiency of semi-implicit and semi-Lagrangian spectral methods for the calculation of incompressible flows

Classical semi-implicit backward Euler/Adams-Baskforth time discretizations of the Navier-Stokes equations induce, for high-Reynolds number flows, sev ere restrictions on the time step. Such restrictions can be relaxed by usin g semi-lagrangian schemes essentially based on splitting the full problem i nto an explicit transport step and an implicit diffusion step. In compariso n 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-implici t' and 'semi-Lagrangian' approaches, in terms of stability, accuracy and co mputational 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. Copyright ( C) 2001 John Wiley & Sons, Ltd.