Abstract
This study assesses the suitability of spectral/hp continuous Galerkin (CG) schemes [1] for model-free under-resolved simulations of a non-trivial turbulent boundary layer flow. We consider a model problem proposed by Spalart in [2] that features a rotating free-stream velocity and admits an asymptotic solution with significant crossflow effects. Note this test case is substantially more complex than typical turbulent boundary layer canonical problems owing to its unsteadiness and enhanced small-scale anisotropy. Reported LES-based solutions to this problem are known to require sophisticated modelling and relatively fine grids to achieve meaningful results, with traditional models exhibiting poor performance. The model-free CG-based approach advocated, on the other hand, yields surprisingly good results with considerably less degrees of freedom for higher order discretisations. Usefully accurate results for the mean flow quantities could even be obtained with half as many degrees of freedom per direction (in comparison to reference LES solutions). Usage of high-order spectral element methods (CG in particular) is therefore strongly motivated for wall-bounded turbulence simulations via under-resolved DNS (uDNS), sometimes called implicit LES (iLES), approaches.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Karniadakis, G.E., Sherwin, S.J.: Spectral/\(hp\) element methods for computational fluid dynamics. Oxford University Press, 2nd edn. Springer (2005)
Spalart, P.R.: Theoretical and numerical study of a three-dimensional turbulent boundary layer. J. Fluid Mech. 205, 319–340 (1989)
Abbà, A., Cercignani, C., et al.: A 3D turbulent boundary layer test for LES models. In: Proceedings of the 1st International Conference on Computational Fluid Dynamics—ICCFD1, pp. 485–490 (2001)
Wu, X., Squires, K.D.: Large eddy simulation of an equilibrium three-dimensional turbulent boundary layer. AIAA J. 35(1), 67–74 (1997)
Cantwell, C.D., Moxey, D., Comerford, A., Bolis, A., Rocco, G., et al.: Nektar++: an open-source spectral/\(hp\) element framework. Comput. Phys. Commun. 192, 205–219 (2015)
Moura, R.C., Sherwin, S.J., Peiró, J.: Eigensolution analysis of spectral/\(hp\) continuous Galerkin approximations to advection-diffusion problems: insights into spectral vanishing viscosity. J. Comput. Phys. 307, 401–422 (2016)
Kirby, R.M., Karniadakis, G.E.: De-aliasing on non-uniform grids: algorithms and applications. J. Comput. Phys. 191, 249–264 (2003)
Moura, R.C., Sherwin, S.J., Peiró, J.: Modified equation analysis for the discontinuous Galerkin formulation. In: Spectral and High Order Methods for PDEs—ICOSAHOM 2014. Springer (2015)
Moura, R.C., Mengaldo, G., Peiró, J., Sherwin, S.J.: An LES setting for DG-based implicit LES with insights on dissipation and robustness. In: Spectral and High Order Methods for PDEs—ICOSAHOM 2016. Springer (2017)
Moura, R.C., Sherwin, S.J., Peiró, J.: Linear dispersion-diffusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral/\(hp\) methods. J. Comput. Phys. 298, 695–710 (2015)
Moura, R.C., Mengaldo, G., Peiró, J., Sherwin, S.J.: On the eddy-resolving capability of high-order discontinuous Galerkin approaches to implicit LES/under-resolved DNS of Euler turbulence. J. Comput. Phys. 330, 615–623 (2017)
Mengaldo, G., Moura, R.C., Giralda, B., Peiró, J., Sherwin, S.J.: Spatial eigensolution analysis of discontinuous Galerkin schemes with practical insights for under-resolved computations and implicit LES. Comput. Fluids 169, 349–364 (2018)
Mengaldo, G., De Grazia, D., Moura, R.C., Sherwin, S.J.: Spatial eigensolution analysis of energy-stable flux reconstruction schemes and influence of the numerical flux on accuracy and robustness. J. Comput. Phys. 358, 1–20 (2018)
Fernandez, P., Moura, R.C., Mengaldo, G., Peraire, J.: Non-modal analysis of spectral element methods: towards accurate and robust large-eddy simulations. Comput. Methods Appl. Mech. 346, 43–62 (2019)
Moura, R.C., Aman, M., Peiró, J., Sherwin, S.J.: Spatial eigenanalysis of spectral/\(hp\) continuous Galerkin schemes and their stabilisation via DG-mimicking spectral vanishing viscosity for high Reynolds number flows. J. Comput. Phys. 406 (2020). https://doi.org/10.1016/j.jcp.2019.109112
Acknowledgements
R. C. Moura would like to acknowledge funding from Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Finance Code 001, under the Brazilian Science without Borders scheme. S. J. Sherwin acknowledges support from EPSRC Platform grant EP/R029423/1. The simulations in this work were performed using the Imperial College Research Computing Service (https://doi.org/10.14469/hpc/2232).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Moura, R.C., Peiró, J., Sherwin, S.J. (2020). Under-Resolved DNS of Non-trivial Turbulent Boundary Layers via Spectral/hp CG Schemes. In: García-Villalba, M., Kuerten, H., Salvetti, M. (eds) Direct and Large Eddy Simulation XII. DLES 2019. ERCOFTAC Series, vol 27. Springer, Cham. https://doi.org/10.1007/978-3-030-42822-8_51
Download citation
DOI: https://doi.org/10.1007/978-3-030-42822-8_51
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-42821-1
Online ISBN: 978-3-030-42822-8
eBook Packages: EngineeringEngineering (R0)