An existence result for a free boundary shallow water model using a lagrangian scheme
An existence result for partially regular weak solutions of certain abstract evolution equations, with an application to magneto-hydrodynamics.
An explicit right inverse of the divergence operator which is continuous in weighted norms
The existence of a continuous right inverse of the divergence operator in , 1 < p < ∞, is a well known result which is basic in the analysis of the Stokes equations. The object of this paper is to show that the continuity also holds for some weighted norms. Our results are valid for Ω ⊂ ℝⁿ a bounded domain which is star-shaped with respect to a ball B ⊂ Ω. The continuity results are obtained by using an explicit solution of the divergence equation and the classical theory of singular integrals...
An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
In this article, we consider the initial value problem which is obtained after a space discretization (with space step ) of the equations governing the solidification process of a multicomponent alloy. We propose a numerical scheme to solve numerically this initial value problem. We prove an error estimate which is not affected by the step size chosen in the space discretization. Consequently, our scheme provides global convergence without any stability condition between and the time step size...
An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
In this article, we consider the initial value problem which is obtained after a space discretization (with space step h) of the equations governing the solidification process of a multicomponent alloy. We propose a numerical scheme to solve numerically this initial value problem. We prove an error estimate which is not affected by the step size h chosen in the space discretization. Consequently, our scheme provides global convergence without any stability condition between h and the time...
An improved regularity criteria for the MHD system based on two components of the solution
As observed by Yamazaki, the third component of the magnetic field can be estimated by the corresponding component of the velocity field in
An indirect boundary integral method for an oscillatory Stokes flow problem.
An initial boundary value problem for Maxwell's equations in a parabolic limit case.
An investigation on gas lift performance curve in an oil-producing well.
An iterative procedure to solve a coupled two-fluids turbulence model
This paper introduces a scheme for the numerical approximation of a model for two turbulent flows with coupling at an interface. We consider the variational formulation of the coupled model, where the turbulent kinetic energy equation is formulated by transposition. We prove the convergence of the approximation to this formulation for 3D flows for large turbulent viscosities and smooth enough flows, whenever bounded in W1,p Sobolev norms for p large enough. Under the same assumptions, we...
An -theory of the generalized Stokes resolvent system in infinite cylinders
Estimates of the generalized Stokes resolvent system, i.e. with prescribed divergence, in an infinite cylinder Ω = Σ × ℝ with , a bounded domain of class , are obtained in the space , q ∈ (1,∞). As a preparation, spectral decompositions of vector-valued homogeneous Sobolev spaces are studied. The main theorem is proved using the techniques of Schauder decompositions, operator-valued multiplier functions and R-boundedness of operator families.
An object-oriented approach to the design of fluid mechanics software
This article presents the guiding principles of the architecture of Trio_U, a new generation of software for thermohydraulic calculations. Trio_U is designed to serve as a thermohydraulic development platform. Its basic conception is object-oriented and it is written in C++. The article demonstrates how this type of design enables an open, modular software architecture.
An object-oriented approach to the design of fluid mechanics software
This article presents the guiding principles of the architecture of Trio_U, a new generation of software for thermohydraulic calculations. Trio_U is designed to serve as a thermohydraulic development platform. Its basic conception is object-oriented and it is written in C++. The article demonstrates how this type of design enables an open, modular software architecture.
An optimal control problem for a generalized Boussinesq model: The time dependent case.
An optimal dimension of submerged parallel bars as a wave reflector.
An optimal method of Galerkin type for diffusion-dispersion problems.
An optimal viscosity profile in the secondary oil recovery
An unconditionally stable finite element-finite volume pressure correction scheme for the drift-flux model
We present in this paper a pressure correction scheme for the drift-flux model combining finite element and finite volume discretizations, which is shown to enjoy essential stability features of the continuous problem: the scheme is conservative, the unknowns are kept within their physical bounds and, in the homogeneous case (i.e. when the drift velocity vanishes), the discrete entropy of the system decreases; in addition, when using for the drift velocity a closure law which takes the form of...
An unconditionally stable pressure correction scheme for the compressible barotropic Navier-Stokes equations
We present in this paper a pressure correction scheme for the barotropic compressible Navier-Stokes equations, which enjoys an unconditional stability property, in the sense that the energy and maximum-principle-based a priori estimates of the continuous problem also hold for the discrete solution. The stability proof is based on two independent results for general finite volume discretizations, both interesting for their own sake: the L2-stability of the discrete advection operator provided it...
An upper bound on the attractor dimension of a 2D turbulent shear flow with a free boundary condition
We consider a free boundary problem of a two-dimensional Navier-Stokes shear flow. There exist a unique global in time solution of the considered problem as well as the global attractor for the associated semigroup. As in [1] and [2], we estimate from above the dimension of the attractor in terms of given data and the geometry of the domain of the flow. This research is motivated by a free boundary problem from lubrication theory where the domain of the flow is usually very thin and the roughness...