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Displaying 81 –
100 of
155
We design efficient numerical schemes for approximating the MHD equations in multi-dimensions. Numerical approximations must be able to deal with the complex wave structure of the MHD equations and the divergence constraint. We propose schemes based on the genuinely multi-dimensional (GMD) framework of [S. Mishra and E. Tadmor, Commun. Comput. Phys. 9 (2010) 688–710; S. Mishra and E. Tadmor, SIAM J. Numer. Anal. 49 (2011) 1023–1045]. The schemes are formulated in terms of vertex-centered potentials....
The paper proposes a general framework allowing the analysis of wetting problems in the
situation when interfacial tensions depend on external fields. An equation predicting
apparent contact angles of sessile droplets deposited on rough surfaces in the presence of
external fields is derived. The problem of wetting is discussed in the framework of the
variational approach. Derivation of a general equation generalizing the Cassie and Wenzel
approaches...
Numerical approximation schemes are discussed for the solution of contaminant transport with adsorption in dual-well flow. The method is based on time stepping and operator splitting for the transport with adsorption and diffusion. The nonlinear transport is solved by Godunov’s method. The nonlinear diffusion is solved by a finite volume method and by Newton’s type of linearization. The efficiency of the method is discussed.
In this paper, we consider an initial boundary value problem for the two-dimensional primitive equations of large scale oceanic dynamics. Assuming that the depth of the ocean is a positive constant, we establish rigorous a priori bounds of the solution to problem. With the aid of these a priori bounds, the continuous dependence of the solution on changes in the boundary terms is obtained.
A nonlinear differential system for describing an air-water system in groundwater hydrology is given. The system is written in a fractional flow formulation, i.e., in terms of a saturation and a global pressure. A continuous-time version of the finite element method is developed and analyzed for the approximation of the saturation and pressure. The saturation equation is treated by a Galerkin finite element method, while the pressure equation is treated by a mixed finite element method. The analysis...
The control of the surface of water in a long canal by means of a wavemaker is investigated. The fluid motion is governed by the Korteweg-de Vries equation in lagrangian coordinates. The null controllability of the elevation of the fluid surface is obtained thanks to a Carleman estimate and some weighted inequalities. The global uncontrollability is also established.
The control of the surface of water in a long canal by
means of a wavemaker is investigated. The fluid motion is governed
by the Korteweg-de Vries equation in Lagrangian coordinates.
The null controllability of the elevation of the fluid surface
is obtained thanks to a Carleman estimate and some weighted inequalities.
The global uncontrollability is also established.
We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .
We wish to show how the shock position in a nozzle could be
controlled. Optimal control theory and algorithm is applied to the
transonic equation. The difficulty is that the derivative with
respect to the shock position involves a Dirac mass. The one
dimensional case is solved, the two dimensional one is analyzed .
In this paper, we investigate the controllability of an underwater vehicle immersed in an infinite volume of an inviscid fluid whose flow is assumed to be irrotational. Taking as control input the flow of the fluid through a part of the boundary of the rigid body, we obtain a finite-dimensional system similar to Kirchhoff laws in which the control input appears through both linear terms (with time derivative) and bilinear terms. Applying Coron’s return method, we establish some local controllability...
Dans ce papier, nous étudions un problème de contrôle par les coefficients issu de la lubrification élastohydrodynamique. La variable de contrôle est l’épaisseur du fluide. Le phénomène de cavitation est pris en compte par le modèle Elrod-Adams, connu pour ses performances dans la conservation des débits d’entrée et de sortie. L’idée est de régulariser dans l’équation d’état le graphe d’Heaviside, en l’approchant par une suite de fonctions monotones et régulières. Nous dérivons les conditions d’optimalité...
The purpose of this paper is to study a control by
coefficients problem issued from the elastohydrodynamic lubrication. The
control variable is the film thickness.The cavitation phenomenon takes place
and described by the Elrod-Adams model, suggested in preference to the
classical variational inequality due to its ability to describe input and
output flow.
The idea is to use the penalization in the state equation by
approximating the Heaviside graph whith a sequence of monotone and regular
functions....
In this paper, we study the
control system associated with the incompressible 3D Euler system.
We show that the velocity field and pressure of the fluid are
exactly controllable in projections by the same finite-dimensional
control. Moreover, the velocity is approximately controllable.
We also prove that 3D Euler
system is not exactly controllable by a finite-dimensional
external force.
In this article, we consider a swimmer (i.e. a self-deformable body) immersed in a fluid, the flow of which is governed by the stationary Stokes equations. This model is relevant for studying the locomotion of microorganisms or micro robots for which the inertia effects can be neglected. Our first main contribution is to prove that any such microswimmer has the ability to track, by performing a sequence of shape changes, any given trajectory in the fluid. We show that, in addition, this can be done...
Currently displaying 81 –
100 of
155