Abstract
Galerkin (spectral) methods for numerical simulation of incompressible flows within simple boundaries are shown to possess many advantages over existing finite-difference methods. In this paper, the accuracy of Galerkin approximations obtained from truncated Fourier expansions is explored. Accuracy of simulation is tested empirically using a simple scalar-convection test problem and the Taylor–Green vortex-decay problem. It is demonstrated empirically that the Galerkin (Fourier) equations involving Np degrees of freedom, where p is the number of space dimensions, give simulations at least as accurate as finite-difference simulations involving (2N)p degrees of freedom. The theoretical basis for the improved accuracy of the Galerkin (Fourier) method is explained. In particular, the nature of aliasing errors is examined in detail. It is shown that ‘aliasing’ errors need not be errors at all, but that aliasing should be avoided in flow simulations. An eigenvalue analysis of schemes for simulation of passive scalar convection supplies the mathematical basis for the improved accuracy of the Galerkin (Fourier) method. A comparison is made of the computational efficiency of Galerkin and finite-difference simulations, and a survey is given of those problems where Galerkin methods are likely to be applied most usefully. We conclude that numerical simulation of many of the flows of current interest is done most efficiently and accurately using the spectral methods advocated here.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Reference38 articles.
1. Fromm, J. E. 1969 Practical investigation of convective difference approximations.Phys. Fluids (suppl. 2)12,3–12.
2. Ellsaesser, H. W. 1966 Evaluation of spectral versus grid methods of hemispheric numerical weather prediction.J. Appl. Meteor.,5,246–262.
3. Phillips, N. A. 1959 An example of non-linear computational instability. The Atmosphere and the Sea in Motion ,501–504.New York:Rockefeller Institute Press.
4. Platzman, G. W. 1961 An approximation to the product of discrete functions.J. Meteor.,18,31–37.
5. Orszag, S. A. 1969 Numerical methods for the simulation of turbulence.Phys. Fluids (suppl. 2)12,250–257.
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