Stochastic modeling of unresolved scales in complex systems |
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Authors: | Jinqiao Duan |
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Affiliation: | 1. Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA; 2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China |
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Abstract: | Model uncertainties or simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., ‘unresolved’) due to a lack in our understanding of these mechanisms or limitations in computational power. The impact of these unresolved scales on the resolved scales needs to be parameterized or taken into account. A stochastic scheme is devised to take the effects of unresolved scales into account, in the context of solving nonlinear partial differential equations. An example is presented to demonstrate this strategy. Dedicated to Professor Peter E. Kloeden on the occasion of his 60th birthday |
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Keywords: | Stochastic partial differential equation (SPDE) stochastic modeling impact of unresolved scales on resolved scales model error large eddy simulation (LES) fractional Brownian motion (fBM) |
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