On the use of biorthogonal interpolating wavelets for large-eddy simulation of turbulence

Marta De la Llave Plata; Stewart Cant; Robert Prosser

doi:10.1016/j.jcp.2012.06.024

On the use of biorthogonal interpolating wavelets for large-eddy simulation of turbulence

Marta De la Llave Plata, Stewart Cant, Robert Prosser

Research output: Contribution to journal › Article › peer-review

Abstract

Recent work in the field of turbulence modelling has demonstrated the benefits of the wavelet-based multiresolution analysis technique as a tool for the formulation of the large-eddy simulation (LES) equations. In this formalism, the LES equations are obtained by projecting the Navier-Stokes equations onto a hierarchy of wavelet spaces. This paper investigates the use of biorthogonal interpolating wavelets as a basis for this projection, placing special emphasis on the wavelet-based differential operators that define this mapping. A detailed analysis of their convergence properties is presented and compared to those of their orthogonal counterpart, the Daubechies wavelets. Based on this study, we highlight the weaknesses of the unlifted interpolating wavelet representation for LES sub-grid modelling. Finally, we establish a link between the unlifted framework and the sampling-based LES approach recently proposed in the literature. © 2012 Elsevier Inc.

Original language	English
Pages (from-to)	6754-6769
Number of pages	15
Journal	Journal of Computational Physics
Volume	231
Issue number	20
DOIs	https://doi.org/10.1016/j.jcp.2012.06.024
Publication status	Published - 15 Aug 2012

Keywords

Interpolating wavelets
Large-eddy simulation
Multiresolution analysis
Sampling operators

Access to Document

10.1016/j.jcp.2012.06.024

Cite this

@article{1662b73dbd8e4f2d866b2f14f1fa75a2,

title = "On the use of biorthogonal interpolating wavelets for large-eddy simulation of turbulence",

abstract = "Recent work in the field of turbulence modelling has demonstrated the benefits of the wavelet-based multiresolution analysis technique as a tool for the formulation of the large-eddy simulation (LES) equations. In this formalism, the LES equations are obtained by projecting the Navier-Stokes equations onto a hierarchy of wavelet spaces. This paper investigates the use of biorthogonal interpolating wavelets as a basis for this projection, placing special emphasis on the wavelet-based differential operators that define this mapping. A detailed analysis of their convergence properties is presented and compared to those of their orthogonal counterpart, the Daubechies wavelets. Based on this study, we highlight the weaknesses of the unlifted interpolating wavelet representation for LES sub-grid modelling. Finally, we establish a link between the unlifted framework and the sampling-based LES approach recently proposed in the literature. {\textcopyright} 2012 Elsevier Inc.",

keywords = "Interpolating wavelets, Large-eddy simulation, Multiresolution analysis, Sampling operators",

author = "{De la Llave Plata}, Marta and Stewart Cant and Robert Prosser",

year = "2012",

month = aug,

day = "15",

doi = "10.1016/j.jcp.2012.06.024",

language = "English",

volume = "231",

pages = "6754--6769",

journal = "Journal of Computational Physics",

issn = "0021-9991",

publisher = "Elsevier BV",

number = "20",

}

TY - JOUR

T1 - On the use of biorthogonal interpolating wavelets for large-eddy simulation of turbulence

AU - De la Llave Plata, Marta

AU - Cant, Stewart

AU - Prosser, Robert

PY - 2012/8/15

Y1 - 2012/8/15

N2 - Recent work in the field of turbulence modelling has demonstrated the benefits of the wavelet-based multiresolution analysis technique as a tool for the formulation of the large-eddy simulation (LES) equations. In this formalism, the LES equations are obtained by projecting the Navier-Stokes equations onto a hierarchy of wavelet spaces. This paper investigates the use of biorthogonal interpolating wavelets as a basis for this projection, placing special emphasis on the wavelet-based differential operators that define this mapping. A detailed analysis of their convergence properties is presented and compared to those of their orthogonal counterpart, the Daubechies wavelets. Based on this study, we highlight the weaknesses of the unlifted interpolating wavelet representation for LES sub-grid modelling. Finally, we establish a link between the unlifted framework and the sampling-based LES approach recently proposed in the literature. © 2012 Elsevier Inc.

AB - Recent work in the field of turbulence modelling has demonstrated the benefits of the wavelet-based multiresolution analysis technique as a tool for the formulation of the large-eddy simulation (LES) equations. In this formalism, the LES equations are obtained by projecting the Navier-Stokes equations onto a hierarchy of wavelet spaces. This paper investigates the use of biorthogonal interpolating wavelets as a basis for this projection, placing special emphasis on the wavelet-based differential operators that define this mapping. A detailed analysis of their convergence properties is presented and compared to those of their orthogonal counterpart, the Daubechies wavelets. Based on this study, we highlight the weaknesses of the unlifted interpolating wavelet representation for LES sub-grid modelling. Finally, we establish a link between the unlifted framework and the sampling-based LES approach recently proposed in the literature. © 2012 Elsevier Inc.

KW - Interpolating wavelets

KW - Large-eddy simulation

KW - Multiresolution analysis

KW - Sampling operators

U2 - 10.1016/j.jcp.2012.06.024

DO - 10.1016/j.jcp.2012.06.024

M3 - Article

SN - 0021-9991

VL - 231

SP - 6754

EP - 6769

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 20

ER -

On the use of biorthogonal interpolating wavelets for large-eddy simulation of turbulence

Abstract

Keywords

Access to Document

Fingerprint

Cite this