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A high-order discontinuous Galerkin method for all-speed flows

Renda, Salvatore and Hartmann, Ralf and De Bartolo, Carmine and Wallraff, Marcel (2015) A high-order discontinuous Galerkin method for all-speed flows. International Journal for Numerical Methods in Fluids, 77 (4), pp. 224-247. Wiley. DOI: 10.1002/fld.3987 ISSN 0271-2091

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Official URL: http://onlinelibrary.wiley.com/doi/10.1002/fld.3987/abstract

Abstract

In this article, we present a discontinuous Galerkin (DG) method designed to improve the accuracy and efficiency of steady solutions of the compressible fully coupled Reynolds-averaged Navier–Stokes and k − ω turbulence model equations for solving all-speed flows. The system of equations is iterated to steady state by means of an implicit scheme. The DG solution is extended to the incompressible limit by implementing a low Mach number preconditioning technique. A full preconditioning approach is adopted, which modifies both the unsteady terms of the governing equations and the dissipative term of the numerical flux function by means of a new preconditioner, on the basis of a modified version of Turkel's preconditioning matrix. At sonic speed the preconditioner reduces to the identity matrix thus recovering the non-preconditioned DG discretization. An artificial viscosity term is added to the DG discretized equations to stabilize the solution in the presence of shocks when piecewise approximations of order of accuracy higher than 1 are used. Moreover, several rescaling techniques are implemented in order to overcome ill-conditioning problems that, in addition to the low Mach number stiffness, can limit the performance of the flow solver. These approaches, through a proper manipulation of the governing equations, reduce unbalances between residuals as a result of the dependence on the size of elements in the computational mesh and because of the inherent differences between turbulent and mean-flow variables, influencing both the evolution of the Courant Friedrichs Lewy (CFL) number and the inexact solution of the linear systems. The performance of the method is demonstrated by solving three turbulent aerodynamic test cases: the flat plate, the L1T2 high-lift configuration and the RAE2822 airfoil (Case 9). The computations are performed at different Mach numbers using various degrees of polynomial approximations to analyze the influence of the proposed numerical strategies on the accuracy, efficiency and robustness of a high-order DG solver at different flow regimes.

Item URL in elib:https://elib.dlr.de/99970/
Document Type:Article
Title:A high-order discontinuous Galerkin method for all-speed flows
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Renda, Salvatoresalvatore.re (at) libero.itUNSPECIFIED
Hartmann, RalfRalf.Hartmann (at) dlr.deUNSPECIFIED
De Bartolo, CarmineUniversity of CalabriaUNSPECIFIED
Wallraff, MarcelMarcel.Wallraff (at) dlr.deUNSPECIFIED
Date:15 February 2015
Journal or Publication Title:International Journal for Numerical Methods in Fluids
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:77
DOI :10.1002/fld.3987
Page Range:pp. 224-247
Editors:
EditorsEmail
Farhat, CharbelUNSPECIFIED
Wall, Wolfgang A.UNSPECIFIED
Publisher:Wiley
ISSN:0271-2091
Status:Published
Keywords:Discontinuous Galerkin methods, Reynolds-Averaged Navier-Stokes equations, low Mach number preconditioning, rescaling techniques, all-speed flows.
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:fixed-wing aircraft
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Simulation and Validation
Location: Braunschweig
Institutes and Institutions:Institute of Aerodynamics and Flow Technology > C²A²S²E - Center for Computer Applications in AeroSpace Science and Engineering
Deposited By: Hartmann, Dr.rer.nat. Ralf
Deposited On:26 Nov 2015 08:33
Last Modified:10 May 2016 23:36

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