کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10356993 | 867842 | 2005 | 20 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Equation-free/Galerkin-free POD-assisted computation of incompressible flows
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موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
We present a Galerkin-free, proper orthogonal decomposition (POD)-assisted computational methodology for numerical simulations of the long-term dynamics of the incompressible Navier-Stokes equations. The approach is based on the “equation-free” framework: we use short, appropriate initialized bursts of full direct numerical simulations (DNS) of the Navier-Stokes equations to observe, estimate, and accelerate, through “projective integration”, the evolution of the flow dynamics. The main assumption is that the long-term dynamics of the flow lie on a low-dimensional, attracting, and invariant manifold, which can be parametrized, not necessarily spanned, by a few POD basis functions. We start with a discussion of the consistency and accuracy of the approach, and then illustrate it through numerical examples: two-dimensional periodic and quasi-periodic flows past a circular cylinder. We demonstrate that the approach can successfully resolve complex flow dynamics at a reduced computational cost and that it can capture the long-term asymptotic state of the flow in cases where traditional Galerkin-POD models fail. The approach trades the overhead involved in developing POD-Galerkin and POD-nonlinear Galerkin codes, for the repeated (yet short, and on demand) use of an existing full DNS simulator. Moreover, since in this approach the POD modes are used to observe rather than span the true system dynamics, the computation is much less sensitive than POD-Galerkin to values of the system parameters (e.g., the Reynolds number) and the particular simulation data ensemble used to obtain the POD basis functions.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 207, Issue 2, 10 August 2005, Pages 568-587
Journal: Journal of Computational Physics - Volume 207, Issue 2, 10 August 2005, Pages 568-587
نویسندگان
Sirod Sirisup, George Em Karniadakis, Dongbin Xiu, Ioannis G. Kevrekidis,