Nonlinear artificial viscosity for spectral element methods

Spectral Vanishing Viscosity Method for Nonlinear

We propose a new spectral viscosity (SV) scheme for the accurate solution of nonlinear conservation laws. It is proved that the SV solution converges to the unique entropy solution under appropriate reasonable conditions. The proposed SV scheme is implemented directly on high modes of the computed solution. This should be compared with the original nonperiodic SV scheme introduced by Maday, Oul...

Stabilisation of spectral/hp element methods through spectral vanishing viscosity: Application to fluid mechanics modelling

In this paper we present a formulation of spectral vanishing viscosity (SVV) for the stabilisation of spectral/hp element methods applied to the solution of the 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 simpl...

Spectral Element Methods for TransitionalFlowsPaul

We describe the development and implementation of an eecient spectral element code for simulating transitional ows in complex three-dimensional domains. Critical to this eeort is the use of geometrically nonconforming elements that allow localized reenement in regions of interest, coupled with a stabilized high-order time-split formulation of the semi-discrete Navier-Stokes equations. Simulatio...

Taming nonlinear instability for discontinuous Galerkin scheme with artificial viscosity

Chebyshev–legendre Spectral Viscosity Method for Nonlinear Conservation Laws∗

In this paper, a Chebyshev–Legendre spectral viscosity (CLSV) method is developed for nonlinear conservation laws with initial and boundary conditions. The boundary conditions are dealt with by a penalty method. The viscosity is put only on the high modes, so accuracy may be recovered by postprocessing the CLSV approximation. It is proved that the bounded solution of the CLSV method converges t...