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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.

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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