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Preconditioned smoothers for the Full Approximation Scheme for the RANS equations

Birken, Philipp ; Bull, Jonathan ; Jameson, Antony

Journal of Scientific Computing, 2018 [Periódico revisado por pares]

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  • Título:
    Preconditioned smoothers for the Full Approximation Scheme for the RANS equations
  • Autor: Birken, Philipp ; Bull, Jonathan ; Jameson, Antony
  • Assuntos: Natural Sciences ; Mathematics ; Computational Mathematics ; Naturvetenskap ; Matematik ; Beräkningsmatematik ; Engineering And Technology ; Mechanical Engineering ; Fluid Mechanics And Acoustics ; Teknik Och Teknologier ; Maskinteknik ; Strömningsmekanik Och Akustik
  • É parte de: Journal of Scientific Computing, 2018
  • Descrição: Byline: Philipp Birken (1), Jonathan Bull (2), Antony Jameson (3) Keywords: Unsteady flows; Multigrid; Discrete Fourier analysis; Runge--Kutta smoothers Abstract: We consider multigrid methods for finite volume discretizations of the Reynolds averaged Navier--Stokes equations for both steady and unsteady flows. We analyze the effect of different smoothers based on pseudo time iterations, such as explicit and additive Runge--Kutta (AERK) methods. Furthermore, by deriving them from Rosenbrock smoothers, we identify some existing schemes as a class of additive W (AW) methods. This gives rise to two classes of preconditioned smoothers, preconditioned AERK and AW, which are implemented the exact same way, but have different parameters and properties. This derivation allows to choose some of these based on results for time integration methods. As preconditioners, we consider SGS preconditioners based on flux vector splitting discretizations with a cutoff function for small eigenvalues. We compare these methods based on a discrete Fourier analysis. Numerical results on pitching and plunging airfoils identify AW3 as the best smoother regarding overall efficiency. Specifically, for the NACA 64A010 airfoil steady-state convergence rates of as low as 0.85 were achieved, or a reduction of 6 orders of magnitude in approximately 25 pseudo-time iterations. Unsteady convergence rates of as low as 0.77 were achieved, or a reduction of 11 orders of magnitude in approximately 70 pseudo-time iterations. Author Affiliation: (1) 0000 0001 0930 2361, grid.4514.4, Centre for the Mathematical Sciences, Numerical Analysis, Lund University, Box 118, Lund, Sweden (2) 0000 0004 1936 9457, grid.8993.b, Division of Scientific Computing, Department of Information Technology, Uppsala University, Box 337, 75105, Uppsala, Sweden (3) 0000000419368956, grid.168010.e, Department of Aeronautics and Astronautics, Stanford University, Stanford, CA, 94305, USA Article History: Registration Date: 24/07/2018 Received Date: 14/10/2017 Accepted Date: 24/07/2018 Online Date: 09/08/2018
  • Idioma: Inglês

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