Design of a Smagorinsky spectral vanishing viscosity turbulence model for discontinuous Galerkin methods. (English) Zbl 1519.76095
Summary: We present a new closure model for Large Eddy Simulation to introduce dissipation in under-resolved turbulent simulation using discontinuous Galerkin (DG) schemes applied to the compressible Navier-Stokes equations. The development of the method is based on a thorough analysis of the numerical dissipation mechanisms in DG schemes. In particular, we use upwind Riemann solvers for inter-element dissipation, and a Spectral Vanishing Viscosity (SVV) method for interior dissipation. First, these mechanisms are analysed using a linear von Neumann analysis (for a linear advection-diffusion equation) to characterise their properties in wave-number space. Second, their behaviour is tested using the three-dimensional Taylor-Green Vortex Navier-Stokes problem to assess transitional/turbulent flows. The results of the study are subsequently used to propose a DG-SVV approach that uses a mode-selection Smagorinsky LES model to compute the turbulent viscosity. When the SVV technique is combined with a low dissipation Riemann solver, the scheme is capable of maintaining low dissipation levels for laminar flows, while providing the correct dissipation for all wave-number ranges in turbulent regimes. The developed approach is designed for polynomial orders \(N \geq 2\) and is specially well suited for high order schemes. This new DG-SVV approach is calibrated with the Taylor-Green test case; to then show its accuracy in an under-resolved (\(y^+ > 8\)) channel flow at Reynolds number \(\mathrm{Re}_\tau = 183\).
MSC:
| 76F65 | Direct numerical and large eddy simulation of turbulence |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
Keywords:
discontinuous Galerkin; energy stable; under-resolved turbulence; large eddy simulation; Smagorinsky; spectral vanishing viscosityReferences:
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