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.

A discontinuous Galerkin method for inviscid low Mach number flows

DE BARTOLO, CARMINE;
2009

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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/153594
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 35
  • ???jsp.display-item.citation.isi??? 29
social impact