Non-linear model reduction for the Navier-Stokes equations using residual DEIM method

JOURNAL OF COMPUTATIONAL PHYSICS

卷:263

Article

Xiao, D.^1,2  Fang, F.¹  Buchan, A. G.¹  Pain, C. C.¹  Navon, I. M.³  Du, J.⁴  Hu, G.² 

[1] Univ London Imperial Coll Sci Technol & Med, Dept Earth Sci & Engn, Appl Modelling & Computat Grp, London SW7 2BP, England

[2] China Univ Geosci, State Key Lab Geol Proc & Mineral Resources, Wuhan 430074, Peoples R China

[3] Florida State Univ, Dept Comp Sci, Tallahassee, FL 32306 USA

[4] Chinese Acad Sci, Inst Atmospher Phys, Beijing 100029, Peoples R China

关键词: Non-linear model reduction;    Empirical interpolation method;    Petrov-Galerkin;    Proper orthogonal decomposition;    Navier-Stokes;   

DOI  :  10.1016/j.jcp.2014.01.011

来源: Elsevier

【 摘 要 】

This article presents a new reduced order model based upon proper orthogonal decomposition (POD) for solving the Navier-Stokes equations. The novelty of the method lies in its treatment of the equation's non-linear operator, for which a new method is proposed that provides accurate simulations within an efficient framework. The method itself is a hybrid of two existing approaches, namely the quadratic expansion method and the Discrete Empirical Interpolation Method (DEIM), that have already been developed to treat non-linear operators within reduced order models. The method proposed applies the quadratic expansion to provide a first approximation of the non-linear operator, and DEIM is then used as a corrector to improve its representation. In addition to the treatment of the non-linear operator the POD model is stabilized using a Petrov-Galerkin method. This adds artificial dissipation to the solution of the reduced order model which is necessary to avoid spurious oscillations and unstable solutions. A demonstration of the capabilities of this new approach is provided by solving the incompressible Navier-Stokes equations for simulating a flow past a cylinder and gyre problems. Comparisons are made with other treatments of non-linear operators, and these show the new method to provide significant improvements in the solution's accuracy. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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