Invited plenary speaker: Sergey V. Utyuzhnikov, a Professor of Computational Mathematics at the University of Manchester, UK
Non-overlapping domain decomposition for near-wall turbulence modelling
Near-wall turbulence modelling is a very computationally expensive problem. The talk considers a novel approach based on non-overlapping domain decomposition [1-5]. It allows us to avoid calculations of the region with high gradients in the vicinity of the wall while retaining sufficient overall accuracy. The technique is introduced in application to low-Reynolds number RANS models. The domain decomposition is achieved via the transfer of the boundary condition from the wall to an interface boundary. If the governing equations in the inner domain are simplified, then the transmission (interface) boundary conditions are of Robin type. These boundary conditions can be obtained in an analytical form despite the fact that they are nonlinear. Possible ways to achieve a reasonable trade-off between efficiency and accuracy are discussed.
The obtained interface boundary conditions are mesh-independent. They can be used to avoid the computationally expensive resolution of a high-gradient region near the wall. Moreover, once the solution is constructed in the outer domain, the near-wall profile can be restored if required. In two extreme cases, if the interface boundary is too close to the wall or too far from it, the so-constructed solution to the problem automatically corresponds to low- and high-Reynolds number models, respectively. Different applications are considered including unsteady problems and complex geometries. The developed approach proved to be quite robust and relatively universal. It does not contain any tuning parameters. It might be extended to other multiscale problems.
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Utyuzhnikov, S.V., “Towards development of unsteady near-wall interface boundary conditions for turbulence modelling”, Computer Physics Communications, 2014, 185 (11): 2879-2884.
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Aleksin, V.A., Utyuzhnikov, S.V., “Implementation of near-wall boundary conditions for modelling boundary layers with free-stream turbulence”, Applied Mathematical Modelling, 2014, 38 (14): 3591-3606.
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Utyuzhnikov, S.V., “Interface boundary conditions in near-wall turbulence modeling”, Computers & Fluids, 2012, 68: 186-191.
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Utyuzhnikov, S.V., “Domain decomposition for near-wall turbulent flows”, Computers & Fluids, 2009, 38 (9): 1710-1717.
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Utyuzhnikov, S.V., “Robin-type wall functions and their numerical implementation”, J. Applied Numerical Mathematics, 2008, 58 (10): 1521-1533.
About the author
Professor Sergey Utyuzhnikov (FIMA) is a Senior Research Fellow at the University of Manchester since 2005 and honorary Professor of Computational Mathematics (Russian Ministry of Education). He is also an Adjunct Professor at the Moscow Institute of Physics and Technology where he gained his PhD in 1986 and DSc in 1997. He has a broad experience in CFD, active sound control, and engineering optimisation acquired over the course of about 30 years. He has given invited talks at Los Alamos National Laboratory, the Royal Society (Kavli Centre), Schlumberger (Cambridge), CARDC (China), EDF/CNRS (Paris), Institut Henri Poincare (Paris), ABB, ALSTOM Ltd (Switzerland), VKI (NATO, Brussels), and numerous international conferences. He is the author or co-author of over 100 peer-reviewed journal publications and many conference papers. In recent years, he has obtained fundamental results related to the generalized potentials theory, non-overlapping domain decomposition, active sound control and nonlinear multi-objective optimisation. He is a co-author (with G.A.Tirskiy) of a recently published book ‘Hypersonic Aerodynamics and Heat Transfer’ (Begell House: ISBN 978-1-56700-309-3).
Professor Utyuzhnikov website can be found under this link