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

✍ Scribed by Chuanju Xu; Richard Pasquetti

• Publisher: John Wiley and Sons
• Year: 2001
• Tongue: English
• Weight: 253 KB
• Volume: 35
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/1097-0363(20010215)35:3<319::aid-fld95>3.0.co;2-v

✦ Synopsis

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.