Abstract
We present recent developments within a high-performance discontinuous Galerkin solver for turbulent incompressible flow. The scheme is based on a high-order semi-explicit temporal approach and high-order spatial discretizations. The implementation is entirely matrix-free, including the global Poisson equation, which makes the solution time per time step essentially independent of the spatial polynomial degree. The algorithm is designed to yield high algorithmic intensities, which enables high efficiency on current and future CPU architectures. The method has previously been applied to DNS and ILES of turbulent channel flow and is in the present work used to compute flow past periodic hills at a hill Reynolds number of \(Re_H=10595\). We also outline our on-going work regarding wall modeling via function enrichment within this framework.
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
Arnold, D.N.: An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19(4), 742–760 (1982). https://doi.org/10.1137/0719052
Bangerth, W., Davydov, D., Heister, T., Heltai, L., Kanschat, G., Kronbichler, M., Maier, M., Turcksin, B., Wells, D.: The deal.II library, version 8.4.0. J. Numer. Math. 24(3), 135–141 (2016). https://doi.org/10.1515/jnma-2016-1045
Fischer, P.F., Lottes, J.W., Kerkemeier, S.: Nek5000 Web page (2016). https://nek5000.mcs.anl.gov
Fröhlich, J., Mellen, C.P., Rodi, W., Temmerman, L., Leschziner, M.A.: Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions. J. Fluid Mech. 526, 19–66 (2005). https://doi.org/10.1017/S0022112004002812
Hindenlang, F., Gassner, G., Altmann, C., Beck, A., Staudenmaier, M., Munz, C.D.: Explicit discontinuous Galerkin methods for unsteady problems. Comput. Fluids 61, 86–93 (2012). https://doi.org/10.1016/j.compfluid.2012.03.006
Karniadakis, G.E., Israeli, M., Orszag, S.A.: High-order splitting methods for the incompressible Navier-Stokes equations. J. Comput. Phys. 97(2), 414–443 (1991). https://doi.org/10.1016/0021-9991(91)90007-8
Karniadakis, G.E., Sherwin, S.J.: Spectral/hp Element Methods for Computational Fluid Dynamics, 2nd edn. Oxford University Press (2005)
Klöckner, A., Warburton, T., Bridge, J., Hesthaven, J.S.: Nodal discontinuous Galerkin methods on graphics processors. J. Comput. Phys. 228(21), 7863–7882 (2009). https://doi.org/10.1016/j.jcp.2009.06.041
Krank, B., Fehn, N., Wall, W.A., Kronbichler, M.: A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow. J. Comput. Phys. 348, 634–659 (2017). https://doi.org/10.1016/j.jcp.2017.07.039
Krank, B., Kronbichler, M., Wall, W.A.: Wall modeling via function enrichment within a high-order DG method for RANS simulations of incompressible flow. Int. J. Numer. Meth. Fluids (2017). https://doi.org/10.1002/fld.4409
Krank, B., Wall, W.A.: A new approach to wall modeling in LES of incompressible flow via function enrichment. J. Comput. Phys. 316, 94–116 (2016). https://doi.org/10.1016/j.jcp.2016.04.001
Kronbichler, M., Kormann, K.: A generic interface for parallel cell-based finite element operator application. Comput. Fluids 63, 135–147 (2012). https://doi.org/10.1016/j.compfluid.2012.04.012
Spalding, D.B.: A single formula for the “law of the wall”. J. Appl. Mech. 28, 455–458 (1961). https://doi.org/10.1115/1.3641728
Acknowledgements
The research presented in this article was partially funded by the German Research Foundation (DFG) under the project “High-order discontinuous Galerkin for the EXA-scale” (ExaDG) within the priority program “Software for Exascale Computing” (SPPEXA), grant agreement no. KR4661/2-1 and WA1521/18-1.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Kronbichler, M., Krank, B., Fehn, N., Legat, S., Wall, W.A. (2018). A New High-Order Discontinuous Galerkin Solver for DNS and LES of Turbulent Incompressible Flow. In: Dillmann, A., et al. New Results in Numerical and Experimental Fluid Mechanics XI. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 136. Springer, Cham. https://doi.org/10.1007/978-3-319-64519-3_42
Download citation
DOI: https://doi.org/10.1007/978-3-319-64519-3_42
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-64518-6
Online ISBN: 978-3-319-64519-3
eBook Packages: EngineeringEngineering (R0)