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

Hald, Ole H. ; Shvets, Yelena ; Stinis, Panagiotis

Lawrence Berkeley National Laboratory

关键词: 99 General And Miscellaneous//Mathematics, Computing, And Information Science;    Two-Dimensional Calculations;    Statistical Mechanics;    Three-Dimensional Calculations;    Convergence;   

DOI  :  10.2172/919384
RP-ID  :  LBNL--61676
RP-ID  :  DE-AC02-05CH11231
RP-ID  :  919384

美国|英语

来源: UNT Digital Library

【 摘 要 】

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.