### Abstract

The solution of the Navier-Stokes equations requires that data about the solution is available along the boundary. In some situations, such as particle imaging velocimetry, there is additional data available along a single plane within the domain, and there is a desire to also incorporate this data into the approximate solution of the Navier-Stokes equation. The question that we seek to answer in this paper is whether two-dimensional velocity data containing noise can be incorporated into a full three-dimensional solution of the Navier-Stokes equations in an appropriate and meaningful way. For addressing this problem, we examine the potential of least-squares finite element methods (LSFEM) because of their flexibility in the enforcement of various boundary conditions. Further, by weighting the boundary conditions in a manner that properly reflects the accuracy with which the boundary values are known, we develop the weighted LSFEM. The potential of weighted LSFEM is explored for three different test problems: the first uses randomly generated Gaussian noise to create artificial 'experimental' data in a controlled manner, and the second and third use particle imaging velocimetry data. In all test problems, weighted LSFEM produces accurate results even for cases where there is significant noise in the experimental data.

Original language | English (US) |
---|---|

Pages (from-to) | 107-118 |

Number of pages | 12 |

Journal | Journal of Computational Physics |

Volume | 229 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2010 |

### Fingerprint

### Keywords

- Data assimilation
- Finite element
- Least-squares
- Particle imaging velocimetry

### ASJC Scopus subject areas

- Computer Science Applications
- Physics and Astronomy (miscellaneous)

### Cite this

*Journal of Computational Physics*,

*229*(1), 107-118. https://doi.org/10.1016/j.jcp.2009.09.016

**Weighted least-squares finite elements based on particle imaging velocimetry data.** / Heys, J. J.; Manteuffel, T. A.; McCormick, S. F.; Milano, M.; Westerdale, J.; Belohlavek, Marek.

Research output: Contribution to journal › Article

*Journal of Computational Physics*, vol. 229, no. 1, pp. 107-118. https://doi.org/10.1016/j.jcp.2009.09.016

}

TY - JOUR

T1 - Weighted least-squares finite elements based on particle imaging velocimetry data

AU - Heys, J. J.

AU - Manteuffel, T. A.

AU - McCormick, S. F.

AU - Milano, M.

AU - Westerdale, J.

AU - Belohlavek, Marek

PY - 2010/1/1

Y1 - 2010/1/1

N2 - The solution of the Navier-Stokes equations requires that data about the solution is available along the boundary. In some situations, such as particle imaging velocimetry, there is additional data available along a single plane within the domain, and there is a desire to also incorporate this data into the approximate solution of the Navier-Stokes equation. The question that we seek to answer in this paper is whether two-dimensional velocity data containing noise can be incorporated into a full three-dimensional solution of the Navier-Stokes equations in an appropriate and meaningful way. For addressing this problem, we examine the potential of least-squares finite element methods (LSFEM) because of their flexibility in the enforcement of various boundary conditions. Further, by weighting the boundary conditions in a manner that properly reflects the accuracy with which the boundary values are known, we develop the weighted LSFEM. The potential of weighted LSFEM is explored for three different test problems: the first uses randomly generated Gaussian noise to create artificial 'experimental' data in a controlled manner, and the second and third use particle imaging velocimetry data. In all test problems, weighted LSFEM produces accurate results even for cases where there is significant noise in the experimental data.

AB - The solution of the Navier-Stokes equations requires that data about the solution is available along the boundary. In some situations, such as particle imaging velocimetry, there is additional data available along a single plane within the domain, and there is a desire to also incorporate this data into the approximate solution of the Navier-Stokes equation. The question that we seek to answer in this paper is whether two-dimensional velocity data containing noise can be incorporated into a full three-dimensional solution of the Navier-Stokes equations in an appropriate and meaningful way. For addressing this problem, we examine the potential of least-squares finite element methods (LSFEM) because of their flexibility in the enforcement of various boundary conditions. Further, by weighting the boundary conditions in a manner that properly reflects the accuracy with which the boundary values are known, we develop the weighted LSFEM. The potential of weighted LSFEM is explored for three different test problems: the first uses randomly generated Gaussian noise to create artificial 'experimental' data in a controlled manner, and the second and third use particle imaging velocimetry data. In all test problems, weighted LSFEM produces accurate results even for cases where there is significant noise in the experimental data.

KW - Data assimilation

KW - Finite element

KW - Least-squares

KW - Particle imaging velocimetry

UR - http://www.scopus.com/inward/record.url?scp=70350377794&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350377794&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2009.09.016

DO - 10.1016/j.jcp.2009.09.016

M3 - Article

AN - SCOPUS:70350377794

VL - 229

SP - 107

EP - 118

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 1

ER -