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On the simulation of nearly inviscid two-dimensional turbulence. (English) Zbl 1159.76031
From the text: We compare two numerical algorithms in a simple test case involving the simulation of two-dimensional freely-decaying turbulence. The first is a standard pseudo-spectral algorithm, as has been widely used in studies of this problem. The second is a less well known hybrid Eulerian-Lagrangian algorithm based on contour dynamics. The comparison verifies the near equivalence, in detail, of the two algorithms at early times. At later times, significant advantages of the second algorithm become clear, in particular the ability to achieve a much higher effective Reynolds number at a negligible fraction of the computational effort. Specifically, a comparable simulation using the pseudo-spectral algorithm would take $${\mathcal O}(10^8)$$ times more computer power.

##### MSC:
 76M22 Spectral methods applied to problems in fluid mechanics 76M25 Other numerical methods (fluid mechanics) (MSC2010) 76F99 Turbulence 76D05 Navier-Stokes equations for incompressible viscous fluids
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