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A discontinuous Galerkin method for inviscid low Mach number flows

Bassi, Francesco and De Bartolo, Carmine and Hartmann, Ralf and Nigro, Alessandra (2009) A discontinuous Galerkin method for inviscid low Mach number flows. Journal of Computational Physics, 228 (11), pp. 3996-4011. Elsevier. DOI: 10.1016/j.jcp.2009.02.021 ISSN 0021-9991

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Official URL: http://ac.els-cdn.com/S0021999109000886/1-s2.0-S0021999109000886-main.pdf?_tid=de7f6ecc-d78f-11e4-b1ba-00000aacb35f&acdnat=1427797544_649e8ffa6304eda339560740a61d057d


In this work we extend the high-order Discontinuous Galerkin (DG) Finite element method to inviscid low Mach number flows. The method here presented is designed to improve the accuracy and efficiency of the solution at low Mach numbers using both explicit and implicit schemes for the temporal discretization of the compressible Euler equations. The algorithm is based on a classical preconditioning technique that in general entails modifying both the instationary term of the governing equations and the dissipative term of the numerical flux function (full preconditioning approach). In the paper we show that full preconditioning is beneficial for explicit time integration while the implicit scheme turns out to be efficient and accurate using just the modified numerical flux function. Thus the implicit scheme could also be used for time accurate computations. The performance of the method is demonstrated by solving an inviscid flow past a NACA0012 airfoil at different low Mach numbers using various degrees of polynomial approximations. Computations with and without preconditioning are performed on different grid topologies to analyze the influence of the spatial discretization on the accuracy of the DG solutions at low Mach numbers.

Item URL in elib:https://elib.dlr.de/61930/
Document Type:Article
Title:A discontinuous Galerkin method for inviscid low Mach number flows
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Bassi, FrancescoUniversity of BergamoUNSPECIFIED
De Bartolo, CarmineUniversity of CalabriaUNSPECIFIED
Hartmann, RalfRalf.Hartmann (at) dlr.deUNSPECIFIED
Nigro, AlessandraUniversity of CalabriaUNSPECIFIED
Journal or Publication Title:Journal of Computational Physics
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In ISI Web of Science:Yes
DOI :10.1016/j.jcp.2009.02.021
Page Range:pp. 3996-4011
Keywords:Low Mach number flow, Discontinuous Galerkin finite element method, preconditioning, Euler equations, compressible flows, Roe scheme
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:Aircraft Research (old)
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Concepts & Integration (old)
Location: Braunschweig
Institutes and Institutions:Institute of Aerodynamics and Flow Technology > CASE
Deposited By: Hartmann, Dr.rer.nat. Ralf
Deposited On:05 Jan 2010 10:20
Last Modified:31 Jul 2019 19:26

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