Method of straight lines for a Bingham problem.
Method of straight lines for a Bingham problem as a model for the flow of waxy crude oils.
Metodi cinetici nello studio qualitativo di problemi di evoluzione nonlineari con convezione e diffusione
Mixed finite element approximation for a coupled petroleum reservoir model
In this paper, we are interested in the modelling and the finite element approximation of a petroleum reservoir, in axisymmetric form. The flow in the porous medium is governed by the Darcy-Forchheimer equation coupled with a rather exhaustive energy equation. The semi-discretized problem is put under a mixed variational formulation, whose approximation is achieved by means of conservative Raviart-Thomas elements for the fluxes and of piecewise constant elements for the pressure and the temperature....
Mixed finite element approximation for a coupled petroleum reservoir model
In this paper, we are interested in the modelling and the finite element approximation of a petroleum reservoir, in axisymmetric form. The flow in the porous medium is governed by the Darcy-Forchheimer equation coupled with a rather exhaustive energy equation. The semi-discretized problem is put under a mixed variational formulation, whose approximation is achieved by means of conservative Raviart-Thomas elements for the fluxes and of piecewise constant elements for the pressure and the temperature....
Modeling, mathematical and numerical analysis of electrorheological fluids
Many electrorheological fluids are suspensions consisting of solid particles and a carrier oil. If such a suspension is exposed to a strong electric field the effective viscosity increases dramatically. In this paper we first derive a model which captures this behaviour. For the resulting system of equations we then prove local in time existence of strong solutions for large data. For these solutions we finally derive error estimates for a fully implicit time-discretization.
Modeling of the resonance of an acoustic wave in a torus
A pneumatic tyre in rotating motion with a constant angular velocity is assimilated to a torus whose generating circle has a radius . The contact of the tyre with the ground is schematized as an ellipse with semi-major axis . When and (where is the velocity of the sound), we show that at the rapid time scale , the air motion within a torus periodically excited on its surface generates an acoustic wave . A study of this acoustic wave is conducted and shows that the mode associated to...
Modelling geophysical flows in the equatorial zone
We present here a series of works which aims at describing geophysical flows in the equatorial zone, taking into account the dominating influence of the earth rotation. We actually proceed by successive approximations computing for each model the response of the fluid to the strong Coriolis penalisation. The main difficulty is due to the spatial variations of the Coriolis acceleration : in particular, as it vanishes at the equator, fast oscillations are trapped in a thin strip of latitudes.
Modelling of the Czochralski flow.
Modelling the Impact of Pericyte Migration and Coverage of Vessels on the Efficacy of Vascular Disrupting Agents
Over the past decade or so, there have been a large number of modelling approaches aimed at elucidating the most important mechanisms affecting the formation of new capillaries from parent blood vessels — a process known as angiogenesis. Most studies have focussed upon the way in which capillary sprouts are initiated and migrate in response to diffusible chemical stimuli supplied by hypoxic stromal cells and leukocytes in the contexts of solid tumour...
Monotone mappings and flows of viscous media.
Monotone solutions of a nonautonomous differential equation for a sedimenting sphere.
Multicomponent models in nuclear astrophysics
We consider hydrodynamical models describing the evolution of a gaseous star in which the presence of thermonuclear reactions between several species leads to a multicomponent formulation. In the case of binary mixtures, recent 3D results are evoked. In the one-dimensional situation, we can prove global estimates and stabilization for some simplified model.
Nested axi-symmetric vortex rings
New unilateral problems in stratigraphy
This work deals with the study of some stratigraphic models for the formation of geological basins under a maximal erosion rate constrain. It leads to introduce differential inclusions of degenerated hyperbolic-parabolic type , where H is the maximal monotonous graph of the Heaviside function and E is a given non-negative function. Firstly, we present the new and realistic models and an original mathematical formulation, taking into account the weather-limited rate constraint in the conservation...
Non blow-up of the 3D ideal magnetohydrodynamics equations for a class of three-dimensional initial data in cylindrical domains.
Non dérivation des équations de Prandtl
Nonclassical Riemann solvers and kinetic relations III: A nonconvex hyperbolic model for Van der Waals fluids.
Nonexistence of Coherent Structures in Two-dimensional Inviscid Channel Flow
Two-dimensional inviscid channel flow of an incompressible fluid is considered. It is shown that if the flow is steady and features no horizontal stagnation, then the flow must necessarily be a parallel shear flow.
Non-existence of global classical solutions to 1D compressible heat-conducting micropolar fluid
We study the non-existence of global classical solutions to 1D compressible heat-conducting micropolar fluid without viscosity. We first show that the life span of the classical solutions with decay at far fields must be finite for the 1D Cauchy problem if the initial momentum weight is positive. Then, we present several sufficient conditions for the non-existence of global classical solutions to the 1D initial-boundary value problem on . To prove these results, some new average quantities are...