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On the development of an implicit high-order Discontinuous Galerkin method for DNS and implicit LES of turbulent flows.

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Title: On the development of an implicit high-order Discontinuous Galerkin method for DNS and implicit LES of turbulent flows.
Authors: Bassi, F.1, Botti, L.1, Colombo, A.1 alessandro.colombo@unibg.it, Crivellini, A.2, Ghidoni, A.3, Massa, F.1
Source: European Journal of Mechanics B: Fluids. Jan2016:Part 2, Vol. 55, p367-379. 13p.
Subjects: Galerkin methods, Discretization methods, Energy dissipation, Navier-Stokes equations, Large eddy simulation models
Abstract: In recent years Discontinuous Galerkin (DG) methods have emerged as one of the most promising high-order discretization techniques for CFD. DG methods have been successfully applied to the simulation of turbulent flows by solving the Reynolds averaged Navier–Stokes (RANS) equations with first-moment closures. More recently, due to their favorable dispersion and dissipation properties, DG discretizations have also been found very well suited for the Direct Numerical Simulation (DNS) and Implicit Large Eddy Simulation (ILES) of turbulent flows. The growing interest in the implementation of DG methods for DNS and ILES is motivated by their attractive features. In particular, these methods can easily achieve high-order accuracy on arbitrarily shaped elements and are perfectly suited to hp -adaptation techniques. Moreover, their compact stencil is independent of the degree of polynomial approximation and is thus well suited for implicit time discretization and for massively parallel implementations. In this paper we focus on recent developments and applications of an implicit high-order DG method for the DNS and ILES of both compressible and incompressible flows. High-order spatial and temporal accuracy has been achieved using the same numerical technology in both cases. Numerical inviscid flux formulations are based on the exact solution of Riemann problems (suitably perturbed in the incompressible case), and viscous flux discretizations rely on the BR2 scheme. Several types of high-order (up to order six) implicit schemes, suited also for DAEs, can be employed for accurate time integration. In particular, linearly implicit Rosenbrock-type Runge–Kutta schemes have been used for all the simulations presented in this work. The massively separated incompressible flow past a sphere at R e D = 1000 , with transition to turbulence in the wake region, is considered as a DNS test case, while the potential of the ILES is demonstrated by computing the compressible transitional flow at R e c = 60 000 , M ∞ = 0.1 and α = 8 ∘ , around the Selig–Donovan 7003 airfoil. The computed solutions are compared with experimental data and numerical results available in the literature, showing good agreement. [ABSTRACT FROM AUTHOR]
Copyright of European Journal of Mechanics B: Fluids is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: On the development of an implicit high-order Discontinuous Galerkin method for DNS and implicit LES of turbulent flows.
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  Data: <searchLink fieldCode="JN" term="%22European+Journal+of+Mechanics+B%3A+Fluids%22">European Journal of Mechanics B: Fluids</searchLink>. Jan2016:Part 2, Vol. 55, p367-379. 13p.
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  Data: <searchLink fieldCode="DE" term="%22Galerkin+methods%22">Galerkin methods</searchLink><br /><searchLink fieldCode="DE" term="%22Discretization+methods%22">Discretization methods</searchLink><br /><searchLink fieldCode="DE" term="%22Energy+dissipation%22">Energy dissipation</searchLink><br /><searchLink fieldCode="DE" term="%22Navier-Stokes+equations%22">Navier-Stokes equations</searchLink><br /><searchLink fieldCode="DE" term="%22Large+eddy+simulation+models%22">Large eddy simulation models</searchLink>
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  Data: In recent years Discontinuous Galerkin (DG) methods have emerged as one of the most promising high-order discretization techniques for CFD. DG methods have been successfully applied to the simulation of turbulent flows by solving the Reynolds averaged Navier–Stokes (RANS) equations with first-moment closures. More recently, due to their favorable dispersion and dissipation properties, DG discretizations have also been found very well suited for the Direct Numerical Simulation (DNS) and Implicit Large Eddy Simulation (ILES) of turbulent flows. The growing interest in the implementation of DG methods for DNS and ILES is motivated by their attractive features. In particular, these methods can easily achieve high-order accuracy on arbitrarily shaped elements and are perfectly suited to hp -adaptation techniques. Moreover, their compact stencil is independent of the degree of polynomial approximation and is thus well suited for implicit time discretization and for massively parallel implementations. In this paper we focus on recent developments and applications of an implicit high-order DG method for the DNS and ILES of both compressible and incompressible flows. High-order spatial and temporal accuracy has been achieved using the same numerical technology in both cases. Numerical inviscid flux formulations are based on the exact solution of Riemann problems (suitably perturbed in the incompressible case), and viscous flux discretizations rely on the BR2 scheme. Several types of high-order (up to order six) implicit schemes, suited also for DAEs, can be employed for accurate time integration. In particular, linearly implicit Rosenbrock-type Runge–Kutta schemes have been used for all the simulations presented in this work. The massively separated incompressible flow past a sphere at R e D = 1000 , with transition to turbulence in the wake region, is considered as a DNS test case, while the potential of the ILES is demonstrated by computing the compressible transitional flow at R e c = 60 000 , M ∞ = 0.1 and α = 8 ∘ , around the Selig–Donovan 7003 airfoil. The computed solutions are compared with experimental data and numerical results available in the literature, showing good agreement. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of European Journal of Mechanics B: Fluids is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.euromechflu.2015.08.010
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      – Code: eng
        Text: English
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        PageCount: 13
        StartPage: 367
    Subjects:
      – SubjectFull: Galerkin methods
        Type: general
      – SubjectFull: Discretization methods
        Type: general
      – SubjectFull: Energy dissipation
        Type: general
      – SubjectFull: Navier-Stokes equations
        Type: general
      – SubjectFull: Large eddy simulation models
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      – TitleFull: On the development of an implicit high-order Discontinuous Galerkin method for DNS and implicit LES of turbulent flows.
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              M: 01
              Text: Jan2016:Part 2
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              Y: 2016
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