A dual‐weighted trust‐region adaptive POD 4‐D Var applied to a finite‐volume shallow water equations model on the sphere

Chen, X.; Akella, Santha; Navon, I. M.

doi:10.1002/fld.2523

Cited by 31 publications

(20 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In a series of papers (see e.g. [31,36,37]) Navon et al proposed a dual-weighted POD method, where the weights assigned to each snapshot were derived from an adjoint related to the optimality system of a variational data assimilation problem in meteorology. It is also known that for compressible flows the choice of inner product and weighting of the different flow variables (velocity, pressure, speed of sound) in the snapshot matrix can have a large effect on the stability and accuracy of the ROM [14,35].…”

Section: "If It Is Not In the Snapshots It Is Not In The Rom"mentioning

confidence: 99%

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

Lassila

Manzoni

Quarteroni

et al. 2014

Reduced Order Methods for Modeling and Computational Reduction

148

179

View full text Add to dashboard Cite

This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities -which are mainly related either to nonlinear convection terms and/or some geometric variability -that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and -in the unsteady case -long-time stability of the reduced model. Moreover, we provide an extensive list of literature references.

show abstract

Section: "If It Is Not In the Snapshots It Is Not In The Rom"mentioning

confidence: 99%

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

Lassila

Manzoni

Quarteroni

et al. 2014

Reduced Order Methods for Modeling and Computational Reduction

148

179

View full text Add to dashboard Cite

show abstract

“…Thus, the inverse background-error covariance cannot be computed numerically. This issue is addressed in our 4D-Var implementation with the approach used in Chen et al (2011), i.e. by applying the change-of-variables transformation δ b (x) = x − x b = B 1/2 z and using z as the control variable.…”

Section: Background-error Covariance Matrixmentioning

confidence: 99%

Impact of non‐smooth observation operators on variational and sequential data assimilation for a limited‐area shallow‐water equation model

Steward

Navon

Zupanski

et al. 2011

Quart J Royal Meteoro Soc

Self Cite

View full text Add to dashboard Cite

We investigate the issue of variational and sequential data assimilation with nonlinear and non-smooth observation operators using a two-dimensional limitedarea shallow-water equation model and its adjoint. The performance of the four-dimensional variational approach (4D-Var: two dimensions plus time) compared with that of the maximum-likelihood ensemble filter (MLEF), a hybrid ensemble/variational method, is tested in the presence of non-smooth observation operators.Following the work of Lewis & Overton and Karmitsa, we investigate minimization of the data-assimilation cost functional using the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) quasi-Newton algorithm originally intended for smooth optimization and the limited-memory bundle method (LMBM) algorithm specifically designed to address large-scale non-smooth minimization problems.Numerical results obtained for the MLEF method show that the LMBM algorithm yields results superior to the L-BFGS method. Results for 4D-Var suggest that L-BFGS performs well when the non-smoothness is not extreme, but fails for nonsmooth functions with large Lipschitz constants. The LMBM method is found to be a suitable choice for large-scale non-smooth optimization, although additional work is needed to improve its numerical stability. Finally, the results and methodologies of 4D-Var and MLEF are compared and contrasted.

show abstract

“…Proper orthogonal decomposition (POD) provides optimal basis for the reduced-order model (ROM) and has many industrial applications, which includes climate modeling of atmospheric and oceanic flows. 2,[4][5][6][7][8][9] Its other applications are structural vibrations, 3, 10, 11 ecosystems, 12 low-dimensional dynamics modeling, 13-17 stochastic partial-differential equations, [18][19][20] and optimization. [21][22][23] The conventional ROM is developed by Galerkin projection of the POD modes onto the governing equations that include heat equation, Burgers equation, and Navier-Stokes equations.…”

Section: Introductionmentioning

confidence: 99%

Proper orthogonal decomposition closure models for Burgers and Navier-Stokes Equations

Imtiaz

Akhtar

Khalid

2015

22nd AIAA Computational Fluid Dynamics Conference

View full text Add to dashboard Cite

Proper orthogonal decomposition based reduced-order models hold importance in fluid dynamics due to their utilization in flow control, design, and optimization. The reducedordered models have shown promising results for laminar flows, however, lack accuracy for complex and turbulent flows. In this study, we consider Burgers and Navier-Stokes equations and develop their reduced order models. Burgers equation is considered with homogenous boundary condition and Navier-Stokes equations are used for simulating the incompressible fluid flow past a circular cylinder. The literature shows that the conventional reduced-order models do not perform well in case of less number of modes and require closure model for the discarded modes. We investigate the effect of closure modeling on the accuracy of the reduced-order model for 1D Burgers equation and 2D Navier-Stokes equations. We consider three mode-dependent closure models, based on eddy viscosity model. This study compares the performance of all considered closure models for wide range of mathematical parameter νe and choose the best closure approach for the reducedorder model of Navier-Stokes equations. The numerical results show that the selected closure model greatly improves the accuracy of the reduced-order model for both Burgers and Navier-Stokes equations.

show abstract

A dual‐weighted trust‐region adaptive POD 4‐D Var applied to a finite‐volume shallow water equations model on the sphere

Cited by 31 publications

References 53 publications

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

Impact of non‐smooth observation operators on variational and sequential data assimilation for a limited‐area shallow‐water equation model

Proper orthogonal decomposition closure models for Burgers and Navier-Stokes Equations

Contact Info

Product

Resources

About