A Parallel Discontinuous Galerkin Code for the Navier-Stokes Equations

Landmann, Björn; Keßler, Manuel; Wagner, Siegfried; Krämer, Ewald

doi:10.2514/6.2006-111

Cited by 20 publications

(28 citation statements)

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“…The high cost of DG methods has motivated several efforts into developing parallel implementations. 6,7 Even though many parts of the computations in the DG method are local and hence natural for a parallel implementation, efficient implicit solvers require the use of preconditioners. Unfortunately, good preconditioners such as incomplete LU factorizations are non-local and of a sequential nature, which make them hard to parallelize.…”

Section: -5mentioning

confidence: 99%

Scalable Parallel Newton-Krylov Solvers for Discontinuous Galerkin Discretizations

Persson

2009

47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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We present techniques for implicit solution of discontinuous Galerkin discretizations of the Navier-Stokes equations on parallel computers. While a block-Jacobi method is simple and straight-forward to parallelize, its convergence properties are poor except for simple problems. Therefore, we consider Newton-GMRES methods preconditioned with block-incomplete LU factorizations, with optimized element orderings based on a minimum discarded fill (MDF) approach. We discuss the difficulties with the parallelization of these methods, but also show that with a simple domain decomposition approach, most of the advantages of the block-ILU over the block-Jacobi preconditioner are still retained. The convergence is further improved by incorporating the matrix connectivities into the mesh partitioning process, which aims at minimizing the errors introduced from separating the partitions. We demonstrate the performance of the schemes for realistic two-and threedimensional flow problems.

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Section: -5mentioning

confidence: 99%

Scalable Parallel Newton-Krylov Solvers for Discontinuous Galerkin Discretizations

Persson

2009

47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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“…Therefore, a three-dimensional Gaussian density fluctuation is initialized in a cuboid domain with straight sided edges, cf. [17]. The pressure and velocity fields are uniform.…”

Section: Gaussian Pulse In Densitymentioning

confidence: 98%

A Comparison of Various Nodal Discontinuous Galerkin Methods for the 3d Euler Equations

Bergmann¹,

Drapkina²,

Ashcroft³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. Recent research has indicated that collocation-type Discontinuous Galerkin Spectral Element Methods (DGSEM) represent a more efficient alternative to the standard modal or nodal DG approaches. In this paper, we compare two collocation-type nodal DGSEM and a standard nodal DG approach in the context of the three-dimensional Euler equations. The nodal DG schemes for hexahedral elements are based on the polynomial interpolation of the unknown solution using tensor product Lagrange basis functions and the use of Gaussian quadrature for integration. In the standard nodal DG approach, we employ uniform interpolation nodes and Legendre-Gauss (LG) quadrature points. The two collocated DGSEM schemes arise from using either LG or Legendre-Gauss-Lobatto (LGL) points as both interpolation and integration nodes. The resulting diagonal mass matrices and the ability to compute the fluxes directly from the solution nodes give rise to highly efficient schemes.The results of the numerical convergence studies highlight, especially at high approximation orders, the performance improvement of the DGSEM schemes compared to the standard DG scheme. Although having advantages in the evaluation of the boundary values over the LG-DGSEM, the lower degree of precision of the LGL quadrature negates this benefit. In addition, without the application of filtering techniques or over-integration, the lower integration accuracy of the LGL-DGSEM leads to numerical instabilities at stagnation points. Hence, the LG-DGSEM is found to be the most efficient scheme as it is more accurate and robust for the considered test cases. 7956

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“…see [14,39,40]). Furthermore, we allow interior elements to be curved in order to avoid the intersection of curved boundary lines with interior elements [7], which might occur for meshes with highly stretched elements as typically used for turbulent flows.…”

Section: The Discontinuous Galerkin Discretizationmentioning

confidence: 99%

“…The past few years have seen considerable progress in the development of higher order and adaptive discontinuous Galerkin (DG) methods for aerodynamic flows [9,[1][2][3][4]7,5,10,6,8]. For example, the European research project ADIGMA [11] concentrated the effort of European scientists on the development of adaptive higher-order variational methods for aerospace applications.…”

Section: Introductionmentioning

confidence: 99%

Adjoint-based error estimation and adaptive mesh refinement for the RANS and k–ω turbulence model equations

Hartmann

Held

Leicht

2011

Journal of Computational Physics

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a b s t r a c tIn this article we present the extension of the a posteriori error estimation and goaloriented mesh refinement approach from laminar to turbulent flows, which are governed by the Reynolds-averaged Navier-Stokes and k-x turbulence model (RANS-kx) equations. In particular, we consider a discontinuous Galerkin discretization of the RANS-kx equations and use it within an adjoint-based error estimation and adaptive mesh refinement algorithm that targets the reduction of the discretization error in single as well as in multiple aerodynamic force coefficients. The accuracy of the error estimation and the performance of the goal-oriented mesh refinement algorithm is demonstrated for various test cases, including a two-dimensional turbulent flow around a three-element high lift configuration and a three-dimensional turbulent flow around a wing-body configuration.

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A Parallel Discontinuous Galerkin Code for the Navier-Stokes Equations

Cited by 20 publications

References 0 publications

Scalable Parallel Newton-Krylov Solvers for Discontinuous Galerkin Discretizations

Scalable Parallel Newton-Krylov Solvers for Discontinuous Galerkin Discretizations

A Comparison of Various Nodal Discontinuous Galerkin Methods for the 3d Euler Equations

Adjoint-based error estimation and adaptive mesh refinement for the RANS and k–ω turbulence model equations

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