Three-level discrete time Galerkin approximations for the non-stationary Navier-Stokes equation
Tin melting: Effect of grid size and scheme on the numerical solution.
Towards robust 3D -pinch simulations: Discretization and fast solvers for magnetic diffusion in heterogeneous conductors.
Transitional vortices in wide-gap spherical annulus flow.
Trapping regions and an ODE-type proof of the existence and uniqueness theorem for Navier-Stokes equations with periodic boundary conditions on the plane.
Tuning the mesh of a mixed method for the stream function. Vorticity formulation of the Navier-Stokes equations.
Two component regularity for the Navier-Stokes equations.
Two dimensional incompressible ideal flow around a thin obstacle tending to a curve
Two-grid finite-element schemes for the steady Navier-Stokes problem in polyhedra.
Two-grid finite-element schemes for the transient Navier-Stokes problem
We semi-discretize in space a time-dependent Navier-Stokes system on a three-dimensional polyhedron by finite-elements schemes defined on two grids. In the first step, the fully non-linear problem is semi-discretized on a coarse grid, with mesh-size . In the second step, the problem is linearized by substituting into the non-linear term, the velocity computed at step one, and the linearized problem is semi-discretized on a fine grid with mesh-size . This approach is motivated by the fact that,...
Two-grid finite-element schemes for the transient Navier-Stokes problem
We semi-discretize in space a time-dependent Navier-Stokes system on a three-dimensional polyhedron by finite-elements schemes defined on two grids. In the first step, the fully non-linear problem is semi-discretized on a coarse grid, with mesh-size H. In the second step, the problem is linearized by substituting into the non-linear term, the velocity uH computed at step one, and the linearized problem is semi-discretized on a fine grid with mesh-size h. This approach is motivated by the fact that,...
Two-Layer Flow with One Viscous Layer in Inclined Channels
We study pressure-driven, two-layer flow in inclined channels with high density and viscosity contrasts. We use a combination of asymptotic reduction, boundary-layer theory and the Karman-Polhausen approximation to derive evolution equations that describe the interfacial dynamics. Two distinguished limits are considered: where the viscosity ratio is small with density ratios of order unity, and where both density and viscosity ratios are small. The evolution equations account for the presence of...
Two-level stabilized nonconforming finite element method for the Stokes equations
In this article, we present a new two-level stabilized nonconforming finite elements method for the two dimensional Stokes problem. This method is based on a local Gauss integration technique and the mixed nonconforming finite element of the pair (nonconforming linear element for the velocity, conforming linear element for the pressure). The two-level stabilized finite element method involves solving a small stabilized Stokes problem on a coarse mesh with mesh size and a large stabilized Stokes...
Un problème de Navier-Stokes avec surface libre et tension superficielle
Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de Navier-Stokes par une technique de projection incrémentale
Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de Navier–Stokes par une technique de projection incrémentale
The Navier–Stokes equations are approximated by means of a fractional step, Chorin–Temam projection method; the time derivative is approximated by a three-level backward finite difference, whereas the approximation in space is performed by a Galerkin technique. It is shown that the proposed scheme yields an error of for the velocity in the norm of l2(L2(Ω)d), where l ≥ 1 is the polynomial degree of the velocity approximation. It is also shown that the splitting error of projection schemes based...
Un résultat de décroissance des poches de tourbillon axisymétriques
Unicité dans L3(R3) et d'autres espaces fonctionnels limites pour Navier-Stokes.
The main result of this paper is the proof of uniqueness for mild solutions of the Navier-Stokes equations in L3(R3). This result is extended as well to some Morrey-Campanato spaces.
Uniqueness of weak solutions of the Navier-Stokes equations
Consider the Navier-Stokes equation with the initial data . Let and be two weak solutions with the same initial value . If satisfies the usual energy inequality and if where is the multiplier space, then we have .
Uniqueness of weak solutions to a Keller-Segel-Navier-Stokes model with a logistic source
We prove a uniqueness result of weak solutions to the Cauchy problem of a Keller-Segel-Navier-Stokes system with a logistic term.