535 research outputs found
Study of full implicit petroleum engineering finite volume scheme for compressible two phase flow in porous media
An industrial scheme, to simulate the two compressible phase flow in porous
media, consists in a finite volume method together with a phase-by-phase
upstream scheme. The implicit finite volume scheme satisfies industrial
constraints of robustness. We show that the proposed scheme satisfy the maximum
principle for the saturation, a discrete energy estimate on the pressures and a
function of the saturation that denote capillary terms. These stabilities
results allow us to derive the convergence of a subsequence to a weak solution
of the continuous equations as the size of the discretization tends to zero.
The proof is given for the complete system when the density of the each phase
depends on the own pressure
Global existence of weak solution to the heat and moisture transport system in fibrous porous media
This paper is concerned with theoretical analysis of a heat and moisture
transfer model arising from textile industries, which is described by a
degenerate and strongly coupled parabolic system. We prove the global (in time)
existence of weak solution by constructing an approximate solution with some
standard smoothing. The proof is based on the physcial nature of gas
convection, in which the heat (energy) flux in convection is determined by the
mass (vapor) flux in convection.Comment: 19 page
Evolution equations in physical chemistry
textWe analyze a number of systems of evolution equations that arise in the study of physical chemistry. First we discuss the well-posedness of a system of mixing compressible barotropic multicomponent flows. We discuss the regularity of these variational solutions, their existence and uniqueness, and we analyze the emergence of a novel type of entropy that is derived for the system of equations.
Next we present a numerical scheme, in the form of a discontinuous Galerkin (DG) finite element method, to model this compressible barotropic multifluid. We find that the DG method provides stable and accurate solutions to our system, and that further, these solutions are energy consistent; which is to say that they satisfy the classical entropy of the system in addition to an additional integral inequality. We discuss the initial-boundary problem and the existence of weak entropy at the boundaries. Next we extend these results to include more complicated transport properties (i.e. mass diffusion), where exotic acoustic and chemical inlets are explicitly shown.
We continue by developing a mixed method discontinuous Galerkin finite element method to model quantum hydrodynamic fluids, which emerge in the study of chemical and molecular dynamics. These solutions are solved in the conservation form, or Eulerian frame, and show a notable scale invariance which makes them particularly attractive for high dimensional calculations.
Finally we implement a wide class of chemical reactors using an adapted discontinuous Galerkin finite element scheme, where reaction terms are analytically integrated locally in time. We show that these solutions, both in stationary and in flow reactors, show remarkable stability, accuracy and consistency.Chemistry and Biochemistr
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