• Corpus ID: 119505364

Lagrangian basis method for dimensionality reduction of convection dominated nonlinear flows

@article{Mojgani2017LagrangianBM,
  title={Lagrangian basis method for dimensionality reduction of convection dominated nonlinear flows},
  author={Rambod Mojgani and Maciej Balajewicz},
  journal={arXiv: Fluid Dynamics},
  year={2017}
}
Foundations of a new projection-based model reduction approach for convection dominated nonlinear fluid flows are summarized. In this method the evolution of the flow is approximated in the Lagrangian frame of reference. Global basis functions are used to approximate both the state and the position of the Lagrangian computational domain. It is demonstrated that in this framework, certain wave-like solutions exhibit low-rank structure and thus, can be efficiently compressed using relatively few… 

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References

SHOWING 1-10 OF 27 REFERENCES

Nonlinear model order reduction based on local reduced‐order bases

A new approach for the dimensional reduction via projection of nonlinear computational models based on the concept of local reduced‐order bases is presented. It is particularly suited for problems

Structure‐preserving, stability, and accuracy properties of the energy‐conserving sampling and weighting method for the hyper reduction of nonlinear finite element dynamic models

The computational efficiency of a typical, projection‐based, nonlinear model reduction method hinges on the efficient approximation, for explicit computations, of the scalar projections onto a

Reduced Order Modeling For High Speed Flows with Moving Shocks

The use of Proper Orthogonal Decomposition for reduced order modeling (POD) of fluid problems is extended to high-speed compressible fluid flows and the robustness of the reduced order models across a wide parameter space is demonstrated.

Spectral analysis of nonlinear flows

We present a technique for describing the global behaviour of complex nonlinear flows by decomposing the flow into modes determined from spectral analysis of the Koopman operator, an

Nonlinear Model Reduction via Discrete Empirical Interpolation

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)

Dynamic mode decomposition of numerical and experimental data

  • P. Schmid
  • Physics, Engineering
    Journal of Fluid Mechanics
  • 2010
The description of coherent features of fluid flow is essential to our understanding of fluid-dynamical and transport processes. A method is introduced that is able to extract dynamic information

Optimal mode decomposition for unsteady flows

The OMD method is shown to be a generalization of dynamic mode decomposition (DMD), in which the subspace is not optimized but rather fixed to be the proper orthogonal decompose (POD) modes.

Reconstruction equations and the Karhunen—Loéve expansion for systems with symmetry