Viscous stabilizations for high order approximations of Saint-Venant and Boussinesq flows

Richard Pasquetti (1, 2)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 CASTOR - Control, Analysis and Simulations for TOkamak Research

Two viscous stabilization methods, namely the spectral vanishing viscosity (SVV) technique and the entropy viscosity method (EVM), are applied to flows of interest in geophysics. First, following a study restricted to one space dimension, the spectral element approximation of the shallow water equations is stabilized using the EVM. Our recent advances are here carefully described. Second, the SVV technique is used for the large-eddy simulation of the spatial and temporal development of the turbulent wake of a sphere in a stratified fluid. We conclude with a parallel between these two stabilization techniques.

Domains: Numerical Analysis [math.NA]; Reactive fluid environment

Richard Pasquetti. Viscous stabilizations for high order approximations of Saint-Venant and Boussinesq flows. ICOSAHOM 2016, Jun 2016, Rio de Janeiro, Brazil. ⟨hal-01361347v2⟩