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

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 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...

Fractional spectral vanishing viscosity method: Application to the quasi-geostrophic equation

We introduce the concept of fractional spectral vanishing viscosity (fSVV) to solve conservations laws that govern the evolution of steep fronts. We apply this method to the two-dimensional surface quasigeostrophic (SQG) equation. The classical solutions of the inviscid SQG equation can develop finite-time singularities. By applying the fSVV method, we are able to simulate these solutions with ...

A Spectral Element Formulation for Fluid - Structure Interactions : Application to Flow Through Collapsible Channels

Vessels in the body are elastic and collapse when the transmural pressure becomes sufficiently negative. Once collapse and subsequent flow limitation occur, these vessels often exhibit self-excited, flow-induced oscillations, commonly referred to as flutter. The exact mechanism behind this phenomenon is not well understood. Solid mechanics capability was added to the computational fluid dynamic...

Introduction to Spectral Element Methods