Large Eddy Simulation with Energy-Conserving Schemes and the Smagorinsky Model: A Note on Accuracy and Computational Efficiency

Dhruv Mehta, Ye Zhang, Alexander Van Zuijlen and Hester Bijl
Additional contact information
Dhruv Mehta: Energy Research Centre of The Netherlands (now TNO), 1755 LE Petten, The Netherlands
Ye Zhang: Aerodynamics, Wind Energy and Propulsion, Delft University of Technology (TU Delft), 2629 HS Delft, The Netherlands
Alexander Van Zuijlen: Aerodynamics, Wind Energy and Propulsion, Delft University of Technology (TU Delft), 2629 HS Delft, The Netherlands
Hester Bijl: Aerodynamics, Wind Energy and Propulsion, Delft University of Technology (TU Delft), 2629 HS Delft, The Netherlands

Energies, 2018, vol. 12, issue 1, 1-25

Abstract: Despite advances in turbulence modelling, the Smagorinsky model remains a popular choice for large eddy simulation (LES) due to its simplicity and ease of use. The dissipation in turbulence energy that the model introduces, is proportional to the Smagorinsky constant, of which many different values have been proposed. These values have been derived for certain simulated test-cases while using a specific set of numerical schemes, to obtain the correct dissipation in energy simply because an incorrect value of the Smagorinsky constant would lead to an incorrect dissipation. However, it is important to bear in mind that numerical codes may suffer from numerical or artificial dissipation, which occurs spuriously through a combination of spatio-temporal and iterative errors. The latter can be controlled through more iterations, the former however, depends on the grid resolution and the time step. Recent research suggests that a complete energy-conserving (EC) spatio-temporal discretisation guarantees zero numerical dissipation for any grid resolution and time step. Therefore, using an EC scheme would ensure that dissipation occurs primarily through the Smagorinsky model (and errors in its implementation) than through the discretisation of the Navier-Stokes (NS) equations. To evaluate the efficacy of these schemes for engineering applications, the article first discusses the use of an EC temporal discretisation as regards to accuracy and computational effort, to ascertain whether EC time advancement is advantageous or not. It was noticed that a simple non-EC explicit method with a smaller time step not only reduces the numerical dissipation to an acceptable level but is computationally cheaper than an implicit-EC scheme for wide range of time steps. Secondly, in terms of spatial discretisation on uniform grids (popular in LES), a simple central-difference scheme is as accurate as an EC spatial discretisation. Finally, following the removal of numerical dissipation with any of the methods mentioned above, one is able to choose a Smagorinsky constant that is nearly independent of the grid resolution (within realistic bounds, for OpenFOAM and an in-house code). This article provides impetus to the efficient use of the Smagorinsky model for LES in fields such as wind farm aerodynamics and atmospheric simulations, instead of more comprehensive and computationally demanding turbulence models.

Keywords: large eddy simulation; energy-conserving schemes; isotropic homogeneous turbulence; Runge-Kutta methods; Smagorinsky model (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/1996-1073/12/1/129/pdf (application/pdf)
https://www.mdpi.com/1996-1073/12/1/129/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jeners:v:12:y:2018:i:1:p:129-:d:194120

Access Statistics for this article

Energies is currently edited by Ms. Agatha Cao

More articles in Energies from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().