Flow, Turbulence and Combustion

, Volume 101, Issue 2, pp 521–551 | Cite as

Direct Numerical Simulation of Flow over Periodic Hills up to \(\text {Re}_{H}= 10{,}595\)

  • Benjamin KrankEmail author
  • Martin Kronbichler
  • Wolfgang A. Wall


We present fully resolved computations of flow over periodic hills at the hill-Reynolds numbers \(\text {Re}_{H}= 5{,}600\) and \(\text {Re}_{H}= 10{,}595\) with the highest fidelity to date. The calculations are performed using spectral incompressible discontinuous Galerkin schemes of \(8^{\text {th}}\) and \(7^{\text {th}}\) order spatial accuracy, \(3^{\text {rd}}\) order temporal accuracy, as well as 34 and 180 million grid points, respectively. We show that the remaining discretization error is small by comparing the results to h- and p-coarsened simulations. We quantify the statistical averaging error of the reattachment length, as this quantity is widely used as an ‘error norm’ in comparing numerical schemes. The results exhibit good agreement with the experimental and numerical reference data, but the reattachment length at \(\text {Re}_{H}= 10{,}595\) is predicted slightly shorter than in the most widely used LES references. In the second part of this paper, we show the broad range of capabilities of the numerical method by assessing the scheme for underresolved simulations (implicit large-eddy simulation) of the higher Reynolds number in a detailed h/p convergence study.


Periodic hill flow Incompressible Navier–Stokes equations Direct numerical simulation Large-eddy simulation High-order discontinuous Galerkin 


Funding Information

Computational resources on SuperMUC in Garching, Germany, provided by the Leibniz Supercomputing Centre, under the project pr83te are gratefully acknowledged. The study was partly 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.

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Computational MechanicsTechnical University of MunichGarchingGermany

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