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Adaptive Turbulence Computation Based on Weak Solutions and Weak Uniqueness

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Quality and Reliability of Large-Eddy Simulations

Part of the book series: Ercoftac Series ((ERCO,volume 12))

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Abstract

We review our work on adaptivity and error control for turbulent flow, and we present recent developments on turbulent boundary layer flow. The computational method G2 is not based on filtering of the Navier-Stokes (NS) equations, and thus no Reynolds (subgrid) stresses are introduced. Instead the mathematical basis is ϵ-weak solutions to the NS equations and weak uniqueness of such ϵ-weak solutions. Based on this mathematical framework we construct adaptive finite element methods for the computation of (mean value) output in turbulent flow, where the mesh is refined with respect to a posteriori estimates of the error in the output of interest. The a posteriori error estimates are based on stability information from the numerical solution of an associated dual (adjoint) problem with data given by the output of interest. To model turbulent boundary layer separation we use a skin friction boundary layer model, and we also consider the case of zero skin friction corresponding to solving the inviscid Euler equations with slip boundary conditions, which we refer to as an EG2 method. The results of EG2 computations suggest a new resolution to the d’Alembert paradox, and a new scenario for turbulent boundary layer separation.

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Author information

Authors and Affiliations

  1. School of Computer Science and Communication, KTH, SE-100 44 Stockholm, Sweden

    Johan Hoffman

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  1. Johan Hoffman
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Editor information

Editors and Affiliations

  1. Div. Applied Mechanics & Energy Conversion, Katholieke Universiteit Leuven, Celestijnenlaan 300A, 3001 Leuven, Heverlee, Belgium

    Johan Meyers

  2. Mathematical Sciences, University of Twente, 7500 AE Enschede, Netherlands

    Bernard J. Geurts

  3. D’Alembert Institute, Universite Paris VI, 4 place Jussieu, 75252 Paris Cedex 5, France

    Pierre Sagaut

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© 2008 Springer-Verlag Berlin Heidelberg

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Hoffman, J. (2008). Adaptive Turbulence Computation Based on Weak Solutions and Weak Uniqueness. In: Meyers, J., Geurts, B.J., Sagaut, P. (eds) Quality and Reliability of Large-Eddy Simulations. Ercoftac Series, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8578-9_2

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