Full and Reduced Order Model Consistency of the Nonlinearity Discretization in Incompressible Flows

@article{Ingimarson2021FullAR,
  title={Full and Reduced Order Model Consistency of the Nonlinearity Discretization in Incompressible Flows},
  author={Sean Ingimarson and Leo G. Rebholz and Traian Iliescu},
  journal={ArXiv},
  year={2021},
  volume={abs/2111.06749}
}
[PDF] Semantic Reader
2 Citations
Highly Influential Citations
1
Methods Citations
1

2 Citations

On the influence of the nonlinear term in the numerical approximation of Incompressible Flows by means of proper orthogonal decomposition methods

It is proved that an additional error term appears in this case, compared with the case in which the same discretization of the nonlinear term is applied for both the FOM and the POD methods.

Consistency of the full and reduced order models for evolve‐filter‐relax regularization of convection‐dominated, marginally‐resolved flows

This paper investigates the role of numerical stabilization in reduced order models (ROMs) of convection-dominated, marginally-resolved flows and investigates the FOM-ROM consistency, i.e., whether the numerical stabilization is beneficial both at the Fom and the ROM level.

References

SHOWING 1-10 OF 51 REFERENCES

A numerical investigation of velocity-pressure reduced order models for incompressible flows

Non-linearly stable reduced-order models for incompressible flow with energy-conserving finite volume methods

Consistency of the full and reduced order models for evolve‐filter‐relax regularization of convection‐dominated, marginally‐resolved flows

This paper investigates the role of numerical stabilization in reduced order models (ROMs) of convection-dominated, marginally-resolved flows and investigates the FOM-ROM consistency, i.e., whether the numerical stabilization is beneficial both at the Fom and the ROM level.

Energy balance and mass conservation in reduced order models of fluid flows

On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows

Several approaches for improving the discrete mass balance or even for computing divergence-free solutions will be discussed: grad-div stabilization, higher order mixed methods derived on the basis of an exact de Rham complex, $H(div)$-conforming finite ...

Structure preserving model order reduction of shallow water equations

Two different approaches for constructing reduced-order models (ROMs) for the two-dimensional shallow water equation (SWE) are presented and it is shown that in both approaches, the invariants of the SWE are preserved over a long period of time, leading to stable solutions.

Introduction to the Numerical Analysis of Incompressible Viscous Flows

This book treats the numerical analysis of finite element computational fluid dynamics. Assuming minimal background, the text covers finite element methods; the derivation, behavior, analysis, and…

A POD-Galerkin reduced order model for a LES filtering approach

On reference solutions and the sensitivity of the 2D Kelvin-Helmholtz instability problem

A reduced order variational multiscale approach for turbulent flows

A reduced order modeling framework for parametrized turbulent flows with moderately high Reynolds numbers within the variational multiscale (VMS) method and the role of inf-sup stabilization by means of supremizers in ROMs based on a VMS formulation is presented.
...