Higher Order Schemes for the Compressible Navier-Stokes Equations

Venkatakrishnan, V.; Allmaras, Steven R.; Kamenetskii, D. S.; Johnson, F. T.

doi:10.2514/6.2003-3987

Cited by 84 publications

(48 citation statements)

References 20 publications

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“…Many issues involving residual convergence were discussed in [1] and to a lesser extent in [14]. We elaborate on one of these issues in this paper, namely the need for the ability to reduce residuals to machine error.…”

Section: Residual Convergencementioning

confidence: 99%

“…Not only must a method survive such grids, but it must reasonably predict where and how to refine or redistribute the grids. A consid- erable effort was expended by the authors in Reference ( [1]) to ensure second order, nonsingular discretizations, but much more needs to be done, especially with respect to higher order methods [14].…”

Section: Residual Convergencementioning

confidence: 99%

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Observations Regarding Algorithms Required for Robust CFD Codes

Johnson

Kamenetskiy

Melvin

et al. 2011

Math. Model. Nat. Phenom.

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Abstract. Over the last three decades Computational Fluid Dynamics (CFD) has gradually joined the wind tunnel and flight test as a primary flow analysis tool for aerodynamic designers. CFD has had its most favorable impact on the aerodynamic design of the high-speed cruise configuration of a transport. This success has raised expectations among aerodynamicists that the applicability of CFD can be extended to the full flight envelope. However, the complex nature of the flows and geometries involved places substantially increased demands on the solution methodology and resources required. Currently most simulations involve Reynolds-Averaged Navier-Stokes (RANS) codes although Large Eddy Simulation (LES) and Detached Eddy Suimulation (DES) codes are occasionally used for component analysis or theoretical studies. Despite simplified underlying assumptions, current RANS turbulence models have been spectacularly successful for analyzing attached, transonic flows. Whether or not these same models are applicable to complex flows with smooth surface separation is an open question. A prerequisite for answering this question is absolute confidence that the CFD codes employed reliably solve the continuous equations involved. Too often, failure to agree with experiment is mistakenly ascribed to the turbulence model rather than inadequate numerics. Grid convergence in three dimensions is rarely achieved. Even residual convergence on a given grid is often inadequate. This paper discusses issues involved in residual and especially grid convergence.

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Section: Residual Convergencementioning

confidence: 99%

Section: Residual Convergencementioning

confidence: 99%

Observations Regarding Algorithms Required for Robust CFD Codes

Johnson

Kamenetskiy

Melvin

et al. 2011

Math. Model. Nat. Phenom.

View full text Add to dashboard Cite

show abstract

“…Oscillations in high order DG schemes can be cured by using slope limiters in the scheme and in recent years a number of authors have contributed to the issue of limiters for DG schemes (e.g. see [8,14,22,24,31,48]). One promising direction of research is design of DG limiters based on weighted essentially non-oscillatory (WENO) finite volume methodology.…”

Section: Nonphysical Oscillations In Higher Order Dg Schemesmentioning

confidence: 99%

“…It is widely recognized in the computational aerodynamics community that implementation of higher order schemes would allows one to enhance the accuracy of a simulation tool and to reduce the number of mesh points. Nevertheless, despite the advantages of higher order schemes, this potentially powerful technology has not been transformed into an industrial CFD code yet [48], and one of the challenging problems that still remains an open question is application of higher order schemes on unstructured meshes generated about complex geometries.…”

Section: Introductionmentioning

confidence: 99%

Application of a Higher Order Discontinuous Galerkin

Wolkov

Hirsch

Petrovskaya

2011

Math. Model. Nat. Phenom.

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Abstract. We discuss the issues of implementation of a higher order discontinuous Galerkin (DG) scheme for aerodynamics computations. In recent years a DG method has intensively been studied at Central Aerohydrodynamic Institute (TsAGI) where a computational code has been designed for numerical solution of the 3-D Euler and Navier-Stokes equations. Our discussion is mainly based on the results of the DG study conducted in TsAGI in collaboration with the NUMECA International. The capacity of a DG scheme to tackle challenging computational problems is demonstrated and its potential advantages over FV schemes widely used in modern computational aerodynamics are highlighted.

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“…However, it is well known that standard, continuous Galerkin methods are unstable for the convection operator [55]. Thus, the solution of the Euler or Navier-Stokes equations requires the addition of a stabilization term, like that used in the Streamwise…”

Section: Background 121 Higher-order Methodsmentioning

confidence: 99%

Multigrid Solution for High-Order Discontinuous Galerkin Discretizations of the Compressible Navier-Stokes Equations

Oliver

Fidkowski

Darmofal

Computational Fluid Dynamics 2004

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Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. AbstractA high-order discontinuous Galerkin finite element discretization and p-multigrid solution procedure for the compressible Navier-Stokes equations are presented. The discretization has an element-compact stencil such that only elements sharing a face are coupled, regardless of the solution space. This limited coupling maximizes the effectiveness of the p-multigrid solver, which relies on an element-line Jacobi smoother. The element-line Jacobi smoother solves implicitly on lines of elements formed based on the coupling between elements in a p = 0 discretization of the scalar transport equation. Fourier analysis of 2-D scalar convection-diffusion shows that the element-line Jacobi smoother as well as the simpler element Jacobi smoother are stable independent of p and flow condition. Mesh refinement studies for simple problems with analytic solutions demonstrate that the discretization achieves optimal order of accuracy of O(h p+1 ). A subsonic, airfoil test case shows that the multigrid convergence rate is independent of p but weakly dependent on h. Finally, higher-order is shown to outperform grid refinement in terms of the time required to reach a desired accuracy level.

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Higher Order Schemes for the Compressible Navier-Stokes Equations

Cited by 84 publications

References 20 publications

Observations Regarding Algorithms Required for Robust CFD Codes

Observations Regarding Algorithms Required for Robust CFD Codes

Application of a Higher Order Discontinuous Galerkin

Multigrid Solution for High-Order Discontinuous Galerkin Discretizations of the Compressible Navier-Stokes Equations

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