Derivation of viscous Saint-Venant system for laminar shallow water

By Jean-Frédéric Gerbeau, Benoit Perthame. 2001

449 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/84be294f6223fc2610f3addd39a16e910d58292a

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In Computational Mechanics

Citations in the corpus

CENTRAL-UPWIND SCHEMES FOR THE SAINT-VENANT SYSTEM (2002, methodology): “More complete systems were recently derived from the Navier-Stokes equations [12].”
ANALYSIS OF A LINEAR FLUID-STRUCTURE INTERACTION PROBLEM (2003, unknown): “, [16]) and the details are omitted.”
On the existence of global weak solutions to the Navier–Stokes equations for viscous compressible and heat conducting fluids (2007, background): “fact, such a viscosity law arises in the physically relevant derivation process of the model in the long wavelength limit [28].”
The generalized Riemann problem method for the shallow water equations with bottom topography (2006, background): “GRP METHODS FOR SHALLOW WATER EQUATIONS WITH BOTTOM TOPOGRAPHY 835 open-channel flow and so on [1, 2].”
Transport of Pollutant in Shallow Water A Two Time Steps Kinetic Method (2003, background): “Gerbeau and Perthame present in [7] a derivation from the Navier–Stokes system.”
A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation* (2009, methodology): “zb u dz, it is well known [11,16,18,20] that the shallow water system (3.”
Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects (2007, methodology): “In the recent article [12] Ferrari and Saleri also uses the main ideas of [ 1 ] to derive a two-dimensional NLSW model.”
Well‐balanced positivity preserving central‐upwind scheme for the shallow water system with friction terms (2015, unknown): “[15,23].”
Existence of Global Weak Solutions for a 2D Viscous Shallow Water Equations and Convergence to the Quasi-Geostrophic Model (2003, methodology): “For System (1), Contrarly to the previous work, the viscous part given by div(hru) and the friction term r 0 u are physically justi ed since they can be derived from the three dimensional Navier-Stokes equations with free surface and friction condition on the bottom, see [15].”
Vanishing of Vacuum States and Blow-up Phenomena of the Compressible Navier-Stokes Equations (2008, methodology): “A one-dimensional compressible flow model, called the viscous Saint-Venant system for laminar shallow water, derived rigorously $hom$ incompressible Navier-Stokes system with a moving free surface by Gerbeau-Perthame recently in [4], has the form:”
Global Existence of Weak Solutions to the Barotropic Compressible Navier-Stokes Flows with Degenerate Viscosities (2015, background): “Recently, a friction shallow-water system, with flat bottom topography, which is derived in [5, 6, 9, 28], can be written in a two-dimensional space domain Ω as (1.”