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797
Models of two phase flows in porous media, used in petroleum
engineering, lead to a system of two coupled equations with elliptic
and parabolic degenerate terms, and two unknowns,
the saturation and the pressure.
For the purpose of their approximation, a coupled scheme, consisting in
a finite volume method together with
a phase-by-phase upstream weighting scheme, is used in the industrial setting.
This paper presents a mathematical analysis of this coupled scheme, first showing
that it satisfies...
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....
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....
A general setting is proposed for the mixed finite element approximations of elliptic differential problems involving a unilateral boundary condition. The treatment covers the Signorini problem as well as the unilateral contact problem with or without friction. Existence, uniqueness for both the continuous and the discrete problem as well as error estimates are established in a general framework. As an application, the approximation of the Signorini problem by the lowest order mixed finite element...
A general setting is proposed for the mixed finite element approximations of
elliptic differential problems involving a unilateral boundary condition. The
treatment covers the Signorini problem as well as the unilateral contact
problem with or without friction. Existence, uniqueness for both the
continuous and the discrete problem as well as error estimates are established
in a general framework. As an application, the approximation of the Signorini
problem by the lowest order mixed finite element...
The numerical solution of the flow of a liquid crystal governed by a particular instance of the Ericksen–Leslie equations is considered. Convergence results for this system rely crucially upon energy estimates which involve norms of the director field. We show how a mixed method may be used to eliminate the need for Hermite finite elements and establish convergence of the method.
The numerical solution of the flow of a liquid crystal governed
by a particular instance of the Ericksen–Leslie equations is considered.
Convergence results for this system rely crucially upon energy
estimates which involve H2(Ω) norms of the director field. We
show how a mixed method may be used to eliminate the need for
Hermite finite elements and establish convergence of the method.
We describe behavior of the air-coal mixture using the Navier–Stokes equations for gas and particle phases, accompanied by a turbulence model. The undergoing chemical reactions are described by the Arrhenian kinetics (reaction rate proportional to where is temperature). We also consider the heat transfer via conduction and radiation. Moreover we use improved turbulence-chemistry interactions for reaction terms. The system of PDEs is discretized using the finite volume method (FVM) and an advection...
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.
There are very few reference solutions in the literature on non-Boussinesq natural convection flows. We propose here a test case problem which extends the well-known De Vahl Davis differentially heated square cavity problem to the case of large temperature differences for which the Boussinesq approximation is no longer valid. The paper is split in two parts: in this first part, we propose as yet unpublished reference solutions for cases characterized by a non-dimensional temperature difference of...
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797