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Some data on the flow of fluids exhibit properties which may not be interpreted with the classic theory of propagation of pressure and of fluids [21] based on the classic D’Arcy’s law which states that the flux is proportional to the pressure gradient. In order to obtain a better representation of the flow and of the pressure of fluids the law of D’Arcy is here modified introducing a memory formalisms operating on the flow as well as on the pressure gradient which implies a filtering of the pressure...
We present a domain decomposition theory on an interface problem for the linear transport equation between a diffusive and a non-diffusive region. To leading order, i.e. up to an error of the order of the mean free path in the diffusive region, the solution in the non-diffusive region is independent of the density in the diffusive region. However, the diffusive and the non-diffusive regions are coupled at the interface at the next order of approximation. In particular, our algorithm avoids iterating...
We present a domain decomposition theory on an interface problem
for the linear transport equation between a diffusive and a non-diffusive region.
To leading order, i.e. up to an error of the order of the mean free path in the
diffusive region, the solution in the non-diffusive region is independent of the
density in the diffusive region. However, the diffusive and the non-diffusive regions
are coupled at the interface at the next order of approximation. In particular, our
algorithm avoids iterating...
A general construction of test functions in the Petrov-Galerkin method is described. Using this construction; algorithms for an approximate solution of the Dirichlet problem for the differential equation are presented and analyzed theoretically. The positive number is supposed to be much less than the discretization step and the values of . An algorithm for the corresponding two-dimensional problem is also suggested and results of numerical tests are introduced.
Waxy Crude Oils (WCO’s) are characterized by the presence of heavy paraffins in
sufficiently large concentrations. They exhibit quite complex thermodynamical and
rheological behaviour and present the peculiar property of giving rise to the formation of
segregated wax deposits, when temperature falls down the so called WAT, or Wax Appearance
Temperature. In extreme cases, segregated waxes may lead to pipeline occlusion due to
deposition on cold walls....
In this paper, we prove the existence of a solution for a quite general stationary compressible Stokes problem including, in particular, gravity effects. The Equation Of State gives the pressure as an increasing superlinear function of the density. This existence result is obtained by passing to the limit on the solution of a viscous approximation of the continuity equation.
The aim of this paper is to give a simple, introductory presentation of the extension of the Virtual Element Method to the discretization of H(div)-conforming vector fields (or, more generally, of (n − 1) − Cochains). As we shall see, the methods presented here can be seen as extensions of the so-called BDM family to deal with more general element geometries (such as polygons with an almost arbitrary geometry). For the sake of simplicity, we limit ourselves to the 2-dimensional case, with the aim...
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, a class of cell centered finite volume schemes,
on general unstructured meshes, for a linear convection-diffusion
problem, is studied. The convection and the diffusion are respectively
approximated by means of an upwind scheme and the so called diamond
cell method [4]. Our main result is an error estimate of
order h, assuming only the W2,p (for p>2) regularity of the
continuous solution, on a mesh of quadrangles. The proof is based on an
extension of the ideas developed in...
We study a finite volume method, used to approximate the solution of the linear two dimensional convection diffusion equation, with mixed Dirichlet and Neumann boundary conditions, on Cartesian meshes refined by an automatic technique (which leads to meshes with hanging nodes). We propose an analysis through a discrete variational approach, in a discrete H1 finite volume space. We actually prove the convergence of the scheme in a discrete H1 norm, with an error estimate of order O(h) (on meshes...
Modeling the kinetics of a precipitation dissolution reaction occurring
in a porous medium where diffusion also
takes place leads to a system of two parabolic equations and one ordinary differential
equation coupled with a stiff reaction term. This system is discretized by a finite
volume scheme which is suitable for the approximation of the
discontinuous reaction term of unknown sign.
Discrete solutions are shown to exist and converge towards a
weak solution of the continuous problem. Uniqueness...
We investigate, in the diffusive scaling, the limit to the macroscopic description of finite-velocity Boltzmann kinetic models, where the rate coefficient in front of the collision operator is assumed to be dependent of the mass density. It is shown that in the limit the flux vanishes, while the evolution of the mass density is governed by a nonlinear parabolic equation of porous medium type. In the last part of the paper we show that our method adapts to prove the so-called Rosseland approximation...
We prove the existence of solutions to two infinite systems of equations obtained by adding a transport term to the classical discrete coagulation-fragmentation system and in a second case by adding transport and spacial diffusion. In both case, the particles have the same velocity as the fluid and in the second case the diffusion coefficients are equal. First a truncated system in size is solved and after we pass to the limit by using compactness properties.
In this paper we present a theory describing the diffusion limited evaporation of sessile
water droplets in presence of contact angle hysteresis. Theory describes two stages of
evaporation process: (I) evaporation with a constant radius of the droplet base; and (II)
evaporation with constant contact angle. During stage (I) the contact angle decreases from
static advancing contact angle to static receding contact angle, during stage (II) the
contact...
In this article we transform a large class of parabolic inverse problems into a nonclassical parabolic equation whose coefficients consist of trace type functionals of the solution and its derivatives subject to some initial and boundary conditions. For this nonclassical problem, we study finite element methods and present an immediate analysis for global superconvergence for these problems, on basis of which we obtain a posteriori error estimators.
Composition gradients in miscible liquids can create volume forces resulting in various
interfacial phenomena. Experimental observations of these phenomena are related to some difficulties
because they are transient, sufficiently weak and can be hidden by gravity driven flows.
As a consequence, the question about their existence and about adequate mathematical models is
not yet completely elucidated. In this work we present some experimental evidences of interfacial
phenomena in miscible liquids...
We propose and analyze a semi Lagrangian method for the
convection-diffusion equation. Error estimates for both semi and
fully discrete finite element approximations are obtained for
convection dominated flows. The estimates are posed in terms of
the projections constructed in [Chrysafinos and Walkington, SIAM J. Numer. Anal. 43 (2006) 2478–2499; Chrysafinos and Walkington, SIAM J. Numer. Anal. 44 (2006) 349–366] and the
dependence of various constants upon the diffusion parameter is
...
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