On the two-dimensional compressible isentropic Navier–Stokes equations

Catherine Giacomoni; Pierre Orenga

Displaying similar documents to “On the two-dimensional compressible isentropic Navier–Stokes equations”

Stabilization methods of bubble type for the -element applied to the incompressible Navier-Stokes equations

Petr Knobloch, Lutz Tobiska (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, a general technique is developed to enlarge the velocity space $V_{h}^{1}$ of the unstable -element by adding spaces $V_{h}^{2}$ such that for the extended pair the Babuska-Brezzi condition is satisfied. Examples of stable elements which can be derived in such a way imply the stability of the well-known -element and the 4-element. However, our new elements are much more cheaper. In particular, we shall see that more than half of the additional degrees of freedom when switching from the...

Finite element approximation of kinetic dilute polymer models with microscopic cut-off

John W. Barrett, Endre Süli (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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We construct a Galerkin finite element method for the numerical approximation of weak solutions to a coupled microscopic-macroscopic bead-spring model that arises from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible Navier–Stokes equations in a bounded domain Ω ⊂ $ℝ^{d}$ , = 2 or 3, for the velocity and the pressure of the fluid, with an elastic extra-stress tensor as right-hand side in the momentum...

Coupling the Stokes and Navier–Stokes equations with two scalar nonlinear parabolic equations

Macarena Gómez Mármol, Francisco Ortegón Gallego (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This work deals with a system of nonlinear parabolic equations arising in turbulence modelling. The unknowns are the components of the velocity field coupled with two scalar quantities and . The system presents nonlinear turbulent viscosity $A (θ, ϕ)$ and nonlinear source terms of the form $θ^{2} {| \nabla u |}^{2}$ and ${θ ϕ | \nabla u |}^{2}$ lying in . Some existence results are shown in this paper, including $L^{\infty}$ -estimates and positivity for both and .

On the Instantaneous Spreading for the Navier–Stokes System in the Whole Space

Lorenzo Brandolese, Yves Meyer (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the spatial behavior of the velocity field of a fluid filling the whole space $^{n}$ ( $n \geq 2$ ) for arbitrarily small values of the time variable. We improve previous results on the spatial spreading by deducing the necessary conditions $\int u_{h} (x, t) u_{k} (x, t) d x = c (t) δ_{h, k}$ under more general assumptions on the localization of . We also give some new examples of solutions which have a stronger spatial localization than in the generic case.