Nonlinear Galerkin method for low-dimensional modeling of fluid dynamic system using POD modes

Kang, Wei; Zhang, Jiazhong; Ren, Xiaobing; Pengfei, Lei

doi:10.1016/j.cnsns.2014.07.030

Cited by 17 publications

(7 citation statements)

References 19 publications

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“…The POD can use snapshots of pollutant distribution simulated by GQSMs, thus, determining the dominant modes of pollutant variation. These dominant modes appropriately present the most representative patterns of STV of pollutant in the simulation period (Kang et al, 2015). To the best of the authors' knowledge, no application has yet been reported aiming to present dominant modes of STV for pollutants in groundwater systems.…”

mentioning

confidence: 85%

A novel model for simulation of nitrate in aquifers

Noori

Dodangeh

Berndtsson

et al. 2018

Preprint

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Abstract. Please Numerical groundwater quality models (GQMs) often run at high computational cost resulting in long simulation times and complex parameter calibration that limit their practical applications. In this study, a novel reduced-order model (ROM) was developed for nitrate simulation in groundwater including a simple structure and with similar accuracy as more extensive GQMs. The proposed methodology for the development of ROM presents a solution for the problem in ROMs developed with eigenvectors, to make predictions into the future. The model performance was investigated by simulation of nitrate in the Karaj Aquifer, Iran. The dominant modes of spatiotemporal variation of nitrate during a five-year period was calculated by the model. The results revealed an excellent agreement between nitrate simulated by the ROM and the well-known Modular Transport 3D Multi Species (MT3DMS). The absolute error between the ROM and the MT3DMS was less than 0.5 mg/l in the most parts of the aquifer. Thus, results confirm that the use of ROM has advantages through a much simpler structure and shorter calculation times. Observed spatiotemporal variation of nitrate in the aquifer was well represented by the ROM simulations. The simplicity of the model makes it highly interesting also to other water resources problems.

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confidence: 85%

A novel model for simulation of nitrate in aquifers

Noori

Dodangeh

Berndtsson

et al. 2018

Preprint

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“…The resulting equations are simple diffusion equations, which can be efficiently solved by standard finite element method. The detailed deduction of the algorithm can be referred to as Kang et al (2012Kang et al ( , 2014Kang et al ( , 2015. Herein only the split procedure of the algorithm is given: I.…”

Section: Ale-cbs Algorithmmentioning

confidence: 99%

Effects of local oscillation of airfoil surface on lift enhancement at low Reynolds number

Kang

Pengfei

Zhang

et al. 2015

Journal of Fluids and Structures

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“…For interaction between low and high modes, Schmidtmann [23] proposed a method using Approximate Inertial Manifolds by approximating the solution of MHD equation examining the behaviour of incompressible fluids. A Nonlinear Galerkin Method for coupling between lower and higher modes using proper orthogonal decomposition approached by Approximate Inertial Manifold was used by Kang et al [24]. Laing et al [25] applied AIMs for post processing calculation to lift the modes of the solution.…”

Section: Introductionmentioning

confidence: 99%

An Improved Model Reduction Method on AIMs for N-S Equations Using Multilevel Finite Element Method and Hierarchical Basis

Aslam¹

2019

NMTMA

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A numerical method is proposed to approach the Approximate Inertial Manifolds (AIMs) in unsteady incompressible Navier-Stokes equations, using multilevel finite element method with hierarchical basis functions. Following AIMS, the unknown variables, velocity and pressure in the governing equations, are divided into two components, namely low modes and high modes. Then, the couplings between low modes and high modes, which are not accounted by standard Galerkin method, are considered by AIMs, to improve the accuracy of the numerical results. Further, the multilevel finite element method with hierarchical basis functions is introduced to approach low modes and high modes in an efficient way. As an example, the flow around airfoil NACA0012 at different angles of attack has been simulated by the method presented, and the comparisons show that there is a good agreement between the present method and experimental results. In particular, the proposed method takes less computing time than the traditional method. As a conclusion, the present method is efficient in numerical analysis of fluid dynamics, especially in computing time.

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Nonlinear Galerkin method for low-dimensional modeling of fluid dynamic system using POD modes

Cited by 17 publications

References 19 publications

A novel model for simulation of nitrate in aquifers

A novel model for simulation of nitrate in aquifers

Effects of local oscillation of airfoil surface on lift enhancement at low Reynolds number

An Improved Model Reduction Method on AIMs for N-S Equations Using Multilevel Finite Element Method and Hierarchical Basis

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