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A spectral vanishing viscosity method for large eddy simulations. (English) Zbl 0984.76036
Summary: A simulation approach for high Reynolds number turbulent flows is developed, combining concepts of monotonicity in nonlinear conservation laws with concepts of large eddy simulation. The spectral vanishing viscosity (SVV) is incorporated into Navier-Stokes equations for controlling high-wavenumber oscillations. Unlike hyperviscosity kernels, the SVV approach involves a second-order operator which can be readily implemented in standard finite element codes. In the work presented here, discretization is performed using hierarchical spectral/hp method accommodating effectively an ab initio intrinsic scale separation. The key result is that the monotonicity is enforced via SVV, leading to stable discretizations without sacrificing the formal accuracy, i.e. exponential convergence. Several examples demonstrate the effectiveness of the approach, including a comparison with eddy-viscosity spectral LES of turbulent channel flow.

MSC:
76F65 Direct numerical and large eddy simulation of turbulence
76M22 Spectral methods applied to problems in fluid mechanics
76M10 Finite element methods applied to problems in fluid mechanics
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