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**A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations.**
*(English)*
Zbl 0871.76040

This paper deals with a high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. We extend a discontinuous finite element discretization originally considered for hyperbolic systems such as the Euler equations to the case of the Navier-Stokes equations by treating the viscous terms with a mixed formulation. The method combines two key ideas which are at the basis of the finite volume and finite element method, the physics of wave propagation being accounted for by means of Riemann problems and accuracy being obtained by means of high-order polynomial approximations within elements. The performance of the method is illustrated by computing the flow on a flat plate and around a NACA0012 airfoil for several flow regimes using constant, linear, quadratic, and cubic elements.

### MSC:

76M10 | Finite element methods applied to problems in fluid mechanics |

76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |

### Keywords:

viscous terms; mixed formulation; Riemann problems; high-order polynomial approximations; flat plate; NACA0012 airfoil
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\textit{F. Bassi} and \textit{S. Rebay}, J. Comput. Phys. 131, No. 2, 267--279 (1997; Zbl 0871.76040)

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### References:

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