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A New High-Order Discontinuous Galerkin Solver for DNS and LES of Turbulent Incompressible Flow

Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design book series (NNFM,volume 136)


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.


  • Discontinuous Galerkin (DG)
  • High-order DG
  • Wall Model
  • Enrichment Functions
  • Turbulent Channel Flow

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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.

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Correspondence to Martin Kronbichler .

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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: , et al. New Results in Numerical and Experimental Fluid Mechanics XI. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 136. Springer, Cham.

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