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

Abstract : 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.
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Richard Pasquetti. Viscous stabilizations for high order approximations of Saint-Venant and Boussinesq flows. Marco Bittencourt; Ney Dumont; Jan S. Hesthaven. Lecture Notes in computational Science and Engineering, 119, Springer, pp.519-531, 2017, Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016, 978-3-319-65870-4. ⟨10.1007/978-3-319-65870-4_37⟩. ⟨hal-01657795⟩

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