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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.

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