A discontinuous Galerkin method for inviscid low Mach number flows
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 discre...
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| Published in | Journal of computational physics Vol. 228; no. 11; pp. 3996 - 4011 |
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| Main Authors | , , , |
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| Language | English |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Bassi, F. De Bartolo, C. Nigro, A. Hartmann, R. |
| Author_xml | – sequence: 1 givenname: F. surname: Bassi fullname: Bassi, F. organization: Dip. di Ingegneria Industriale, Università di Bergamo, viale Marconi 5, 24044 Dalmine, BG, Italy – sequence: 2 givenname: C. surname: De Bartolo fullname: De Bartolo, C. email: c.debartolo@unical.it organization: Dipartimento di Meccanica, Università della Calabria, Ponte P. Bucci cubo 44/C, 87036 Rende, CS, Italy – sequence: 3 givenname: R. surname: Hartmann fullname: Hartmann, R. organization: Institute of Aerodynamics and Flow Technology, German Aerospace Center (DLR), Lilienthalplatz 7, 38108 Braunschweig, Germany – sequence: 4 givenname: A. surname: Nigro fullname: Nigro, A. organization: Dipartimento di Meccanica, Università della Calabria, Ponte P. Bucci cubo 44/C, 87036 Rende, CS, Italy |
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| Keywords | Low Mach number flows Euler equations Discontinuous Galerkin finite element method Roe scheme Preconditioning Compressible flows Polynomial approximation Topology Calculation methods Galerkin-Petrov method Finite element method Algorithms Discretization Calculation Performance Compressible flow Mach number |
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| SubjectTerms | Compressible flows Computational techniques Discontinuous Galerkin finite element method Euler equations Exact sciences and technology Low Mach number flows Mathematical methods in physics Physics Preconditioning Roe scheme |
| Title | A discontinuous Galerkin method for inviscid low Mach number flows |
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