Application of the t-model of optimal prediction to the estimationof the rate of decay of solutions of the Euler equations in two and threedimensions

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The "t-model" for dimensional reduction is applied to theestimation of the rate of decay of solutions of the Burgers equation andof the Euler equations in two and three space dimensions. The model wasfirst derived in a statistical mechanics context, but here we analyze itpurely as a numerical tool and prove its convergence. In the Burgers casethe model captures the rate of decay exactly, as was already previouslyshown. For the Euler equations in two space dimensions, the modelpreserves energy as it should. In three dimensions, we find a power lawdecay in time and observe a temporal intermittency.

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Hald, Ole H.; Shvets, Yelena & Stinis, Panagiotis October 7, 2006.

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The "t-model" for dimensional reduction is applied to theestimation of the rate of decay of solutions of the Burgers equation andof the Euler equations in two and three space dimensions. The model wasfirst derived in a statistical mechanics context, but here we analyze itpurely as a numerical tool and prove its convergence. In the Burgers casethe model captures the rate of decay exactly, as was already previouslyshown. For the Euler equations in two space dimensions, the modelpreserves energy as it should. In three dimensions, we find a power lawdecay in time and observe a temporal intermittency.

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  • Report No.: LBNL--61676
  • Grant Number: DE-AC02-05CH11231
  • DOI: 10.2172/919384 | External Link
  • Office of Scientific & Technical Information Report Number: 919384
  • Archival Resource Key: ark:/67531/metadc888083

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  • October 7, 2006

Added to The UNT Digital Library

  • Sept. 22, 2016, 2:13 a.m.

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  • Dec. 13, 2016, 8:54 p.m.

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Hald, Ole H.; Shvets, Yelena & Stinis, Panagiotis. Application of the t-model of optimal prediction to the estimationof the rate of decay of solutions of the Euler equations in two and threedimensions, report, October 7, 2006; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc888083/: accessed November 19, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.