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On the two-dimensional compressible isentropic Navier–Stokes equations

Catherine Giacomoni;  Pierre Orenga — 2002

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We analyze the compressible isentropic Navier–Stokes equations (Lions, 1998) in the two-dimensional case with γ = c p / c v = 2 . These equations also modelize the shallow water problem in height-flow rate formulation used to solve the flow in lakes and perfectly well-mixed sea. We establish a convergence result for the time-discretized problem when the momentum equation and the continuity equation are solved with the Galerkin method, without adding a penalization term in the continuity equation as it is made in...

On the two-dimensional compressible isentropic Navier–Stokes equations

Catherine Giacomoni;  Pierre Orenga — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

We analyze the compressible isentropic Navier–Stokes equations (Lions, 1998) in the two-dimensional case with γ = c p / c v = 2 . These equations also modelize the shallow water problem in height-flow rate formulation used to solve the flow in lakes and perfectly well-mixed sea. We establish a convergence result for the time-discretized problem when the momentum equation and the continuity equation are solved with the Galerkin method, without adding a penalization term in the continuity equation as it is made in Lions...

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