POD/DEIM nonlinear model order reduction of an ADI implicit shallow water equations model
R. ŞTefnescu,Ionel Michael Navon +1 more
TLDR
Numerical tests revealed that if the number of points selected by DEIM algorithm reached 50, the approximation errors due to POD/DEIM and POD reduced systems have the same orders of magnitude, thus supporting the theoretical results existing in the literature.About:
This article is published in Journal of Computational Physics.The article was published on 2013-03-01 and is currently open access. It has received 147 citations till now. The article focuses on the topics: Discretization & Finite difference method.read more
Citations
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Non-linear model reduction for the Navier-Stokes equations using residual DEIM method
TL;DR: This article presents a new reduced order model based upon proper orthogonal decomposition (POD) for solving the Navier-Stokes equations that is a hybrid of two existing approaches, namely the quadratic expansion method and the Discrete Empirical Interpolation Method (DEIM).
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Non-intrusive reduced-order modelling of the Navier-Stokes equations based on RBF interpolation
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A numerical investigation of velocity-pressure reduced order models for incompressible flows
TL;DR: It turns out that the two ROMs that utilize pressure modes are superior to the ROM that uses only velocity modes, both in terms of reproducing the results of the underlying simulations for obtaining the snapshots and of efficiency.
Journal ArticleDOI
Non-intrusive reduced order modelling of the Navier-Stokes equations
D. Xiao,D. Xiao,Fangxin Fang,Andrew G. Buchan,Christopher C. Pain,Ionel Michael Navon,Ann Muggeridge +6 more
TL;DR: Two new non-intrusive reduced order models based upon proper orthogonal decomposition (POD) for solving the Navier–Stokes equations are presented and it is demonstrated that accuracy relative to the high fidelity model is maintained whilst CPU times are reduced by several orders of magnitude in comparison to high fidelity models.
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An improved algorithm for the shallow water equations model reduction: Dynamic Mode Decomposition vs POD
TL;DR: In this article, an improved framework for dynamic mode decomposition (DMD) of 2-D flows for problems originating from meteorology was proposed, where a large time step acts like a filter in obtaining the significant Koopman modes, therefore, the classic DMD method is not effective.
References
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Nonlinear Model Reduction via Discrete Empirical Interpolation
TL;DR: A dimension reduction method called discrete empirical interpolation is proposed and shown to dramatically reduce the computational complexity of the popular proper orthogonal decomposition (POD) method for constructing reduced-order models for time dependent and/or parametrized nonlinear partial differential equations (PDEs).
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Computational Design for Long-Term Numerical Integration of the Equations of Fluid Motion
TL;DR: In this article, it was shown that the derived form of the finite difference Jacobian can prevent nonlinear computational instability and thereby permit long-term numerical integrations, which is not the case in finite difference analogues of the equation of motion for two-dimensional incompressible flow.
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An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations
TL;DR: Barrault et al. as discussed by the authors presented an efficient reduced-basis discretization procedure for partial differential equations with nonaffine parameter dependence, replacing non-affine coefficient functions with a collateral reducedbasis expansion, which then permits an affine offline-online computational decomposition.
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A hierarchy of low-dimensional models for the transient and post-transient cylinder wake
TL;DR: A hierarchy of low-dimensional Galerkin models is proposed for the viscous, incompressible flow around a circular cylinder building on the pioneering works of Stuart (1958), Deane et al. (1991), and Ma & Karniadakis (2002) as mentioned in this paper.