### Abstract

Results are presented from a new approach to modeling the subgrid-scale stresses in large-eddy simulation of turbulent flows, based on explicit evaluation of the subgrid velocity components from a multifractal representation of the subgrid vorticity field. The approach is motivated by prior studies showing that the enstrophy field exhibits multifractal scale-similarity on inertial-range scales in high Reynolds number turbulence. A scale-invariant multiplicative cascade thus gives the spatial distribution of subgrid vorticity magnitudes within each resolved-scale cell, and an additive cascade gives the progressively isotropic decorrelation of subgrid vorticity orientations from the resolved scale Δ to the viscous scale λ_{ν}. The subgrid velocities are then obtained from Biot-Savart integrals over this subgrid vorticity field. The resulting subgrid velocity components become simple algebraic expressions in terms of resolved-scale quantities, which then allow explicit evaluation of the subgrid stresses τ_{ij}*. This new multifractal subgrid-scale model is shown in a priori tests to give good agreement for the filtered subgrid velocities, the subgrid stress components, and the subgrid energy production at both low (Re_{Δ}; ≈ 160) and high (Re_{Δ}; ≈ 2550) resolved-scale Reynolds numbers. Implementing the model is no more computationally burdensome than traditional eddy-viscosity models. Moreover, evaluation of the subgrid stresses requires no explicit differentiation of the resolved velocity field and is therefore comparatively unaffected by discretization errors.

Original language | English (US) |
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Pages (from-to) | 1-16 |

Number of pages | 16 |

Journal | Physics of Fluids |

Volume | 17 |

Issue number | 7 |

DOIs | |

State | Published - Jul 2005 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Mechanics of Materials
- Computational Mechanics
- Physics and Astronomy(all)
- Fluid Flow and Transfer Processes
- Condensed Matter Physics

### Cite this

**Multifractal subgrid-scale modeling for large-eddy simulation. I. Model development and a priori testing.** / Burton, Gregory C.; Dahm, Werner.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 17, no. 7, pp. 1-16. https://doi.org/10.1063/1.1965058

}

TY - JOUR

T1 - Multifractal subgrid-scale modeling for large-eddy simulation. I. Model development and a priori testing

AU - Burton, Gregory C.

AU - Dahm, Werner

PY - 2005/7

Y1 - 2005/7

N2 - Results are presented from a new approach to modeling the subgrid-scale stresses in large-eddy simulation of turbulent flows, based on explicit evaluation of the subgrid velocity components from a multifractal representation of the subgrid vorticity field. The approach is motivated by prior studies showing that the enstrophy field exhibits multifractal scale-similarity on inertial-range scales in high Reynolds number turbulence. A scale-invariant multiplicative cascade thus gives the spatial distribution of subgrid vorticity magnitudes within each resolved-scale cell, and an additive cascade gives the progressively isotropic decorrelation of subgrid vorticity orientations from the resolved scale Δ to the viscous scale λν. The subgrid velocities are then obtained from Biot-Savart integrals over this subgrid vorticity field. The resulting subgrid velocity components become simple algebraic expressions in terms of resolved-scale quantities, which then allow explicit evaluation of the subgrid stresses τij*. This new multifractal subgrid-scale model is shown in a priori tests to give good agreement for the filtered subgrid velocities, the subgrid stress components, and the subgrid energy production at both low (ReΔ; ≈ 160) and high (ReΔ; ≈ 2550) resolved-scale Reynolds numbers. Implementing the model is no more computationally burdensome than traditional eddy-viscosity models. Moreover, evaluation of the subgrid stresses requires no explicit differentiation of the resolved velocity field and is therefore comparatively unaffected by discretization errors.

AB - Results are presented from a new approach to modeling the subgrid-scale stresses in large-eddy simulation of turbulent flows, based on explicit evaluation of the subgrid velocity components from a multifractal representation of the subgrid vorticity field. The approach is motivated by prior studies showing that the enstrophy field exhibits multifractal scale-similarity on inertial-range scales in high Reynolds number turbulence. A scale-invariant multiplicative cascade thus gives the spatial distribution of subgrid vorticity magnitudes within each resolved-scale cell, and an additive cascade gives the progressively isotropic decorrelation of subgrid vorticity orientations from the resolved scale Δ to the viscous scale λν. The subgrid velocities are then obtained from Biot-Savart integrals over this subgrid vorticity field. The resulting subgrid velocity components become simple algebraic expressions in terms of resolved-scale quantities, which then allow explicit evaluation of the subgrid stresses τij*. This new multifractal subgrid-scale model is shown in a priori tests to give good agreement for the filtered subgrid velocities, the subgrid stress components, and the subgrid energy production at both low (ReΔ; ≈ 160) and high (ReΔ; ≈ 2550) resolved-scale Reynolds numbers. Implementing the model is no more computationally burdensome than traditional eddy-viscosity models. Moreover, evaluation of the subgrid stresses requires no explicit differentiation of the resolved velocity field and is therefore comparatively unaffected by discretization errors.

UR - http://www.scopus.com/inward/record.url?scp=23044440156&partnerID=8YFLogxK

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U2 - 10.1063/1.1965058

DO - 10.1063/1.1965058

M3 - Article

VL - 17

SP - 1

EP - 16

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 7

ER -