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International Journal for Multiscale Computational Engineering
インパクトファクター: 1.016 5年インパクトファクター: 1.194 SJR: 0.554 SNIP: 0.82 CiteScore™: 2

ISSN 印刷: 1543-1649
ISSN オンライン: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2012004317
pages 93-116

AN OPTIMAL PREDICTION METHOD FOR UNDERRESOLVED TIME-MARCHING AND TIME-SPECTRAL

Allen LaBryer
Department of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, Oklahoma
Peter J. Attar
Department of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, Oklahoma
Prakash Vedula
Department of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, Oklahoma

要約

The prevalence of multiscale phenomena in nonlinear dynamical systems often necessitates the use of reduced-order models. Similar in concept to the traditional view of spatial reduced-order models, under-resolved time-discretization schemes may be used to decrease the computational burden while sacrificing some level of accuracy. We present a framework based on the optimal prediction formalism that can be used to minimize the errors intrinsic to any timediscretization scheme. Models will be developed for the unresolved subgrid-scale dynamics and added to the governing equations. These subgrid-scale models will interact with the resolved timescales as the system evolves, rendering the optimal solution with respect to the chosen resolution. To demonstrate the technique, we study the van der Pol oscillator using a well-known time-marching scheme and a novel time-spectral method.


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