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Evaluation of a high-order discontinuous Galerkin method for the DNS of turbulent flows. (English) Zbl 1391.76209
Summary: The purpose of this paper is to assess the accuracy of a discontinuous Galerkin (DG) method for the direct numerical simulation (DNS) of freely decaying and wall-bounded turbulent flows. The 2D dipole-wall collision problem, the 3D Taylor-Green vortex flow, and the turbulent channel flow are considered. The results of the DG-based DNS are compared with reference data from DNS based on classical pseudo-spectral methods. For all three configurations the high-order DG method is found to predict accurately second-order statistics. The tests show that the level of accuracy provided by high-order DG discretizations is comparable to that of spectral methods for an equivalent number of degrees of freedom. Emphasis is placed on the benefits of increasing the polynomial order, $$p$$, over increasing the mesh resolution, $$h$$. A detailed $$hp$$-convergence study for the dipole-wall configuration reveals that an order of approximation higher than $$2 (p>1)$$ is necessary to obtain accurate results at minimum computational cost.

##### MSC:
 76F65 Direct numerical and large eddy simulation of turbulence 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 76D05 Navier-Stokes equations for incompressible viscous fluids 76M10 Finite element methods applied to problems in fluid mechanics
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