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On the efficiency of semi‐implicit and semi‐Lagrangian spectral methods for the calculation of incompressible flows
Author(s) -
Xu Chuanju,
Pasquetti Richard
Publication year - 2001
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/1097-0363(20010215)35:3<319::aid-fld95>3.0.co;2-v
Subject(s) - mathematics , euler's formula , spectral method , collocation (remote sensing) , euler equations , compressibility , computational fluid dynamics , advection , stability (learning theory) , lagrangian , navier–stokes equations , pressure correction method , reynolds number , explicit and implicit methods , mathematical analysis , collocation method , turbulence , mechanics , computer science , physics , differential equation , ordinary differential equation , machine learning , thermodynamics
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. Copyright © 2001 John Wiley & Sons, Ltd.