Viscous Stabilizations for High Order Approximations of Saint-Venant and Boussinesq Flows
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.
Part of this work was made at the Dpt of Mathematics of National Taiwan University in the frame of the Inria project AMOSS.
- 6.J.-L. Guermond, A. Larios, T. Thompson, Validation of an entropy-viscosity model for large eddy simulation. Direct and Large Eddy-Eddy Simulation IX, ECOFTAC Series 20, 43–48 (2015)Google Scholar
- 7.J.-L. Guermond, R. Pasquetti, Entropy-based nonlinear viscosity for Fourier approximations of conservation laws. C.R. Acad. Sci. Paris Ser. I 346, 801–806 (2008)Google Scholar
- 19.R. Pasquetti, J.L. Guermond, B. Popov, Stabilized spectral element approximation of the Saint-Venant system using the entropy viscosity technique, in Lecture Notes in computational Science and Engineering: Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2014, vol. 106 (Springer, Berlin, 2015), pp. 397–404zbMATHGoogle Scholar