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Stabilisation of spectral/\(hp\) element methods through spectral vanishing viscosity: Application to fluid mechanics modelling. (English) Zbl 1115.76060
Summary: We present a formulation of spectral vanishing viscosity (SVV) for the stabilisation of spectral/\(hp\) element methods applied to the solution of incompressible Navier-Stokes equations. We construct the SVV around a filter with respect to an orthogonal expansions, and prove that this methodology provides a symmetric semi-positive definite SVV operator. After providing a few simple one- and two-dimensional examples to demonstrate the utility of the SVV, we examine how it can be applied to a spectral/\(hp\) element discretisation of Navier-Stokes equations using a velocity correction splitting scheme. We provide three fluid flow examples to illustrate the pros and cons of this approach in terms of stability and accuracy.

76M22 Spectral methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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