Mathematics – Analysis of PDEs
Scientific paper
2006-10-08
Mathematics
Analysis of PDEs
14 pages, 6 figures. This is the companion paper to math.NA/0607108
Scientific paper
The "t-model" for dimensional reduction is applied to the estimation of the rate of decay of solutions of the Burgers equation and of the Euler equations in two and three space dimensions. The model was first derived in a statistical mechanics context, but here we analyze it purely as a numerical tool and prove its convergence. In the Burgers case the model captures the rate of decay exactly, as was already previously shown. For the Euler equations in two space dimensions, the model preserves energy as it should. In three dimensions, we find a power law decay in time and observe a temporal intermittency.
Hald Ole H.
Stinis Panagiotis
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