Type Equation (type + equation)

Distribution by Scientific Domains


Selected Abstracts


Some results on the accuracy of an edge-based finite volume formulation for the solution of elliptic problems in non-homogeneous and non-isotropic media

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2009
Darlan Karlo Elisiário de Carvalho
Abstract The numerical simulation of elliptic type problems in strongly heterogeneous and anisotropic media represents a great challenge from mathematical and numerical point of views. The simulation of flows in non-homogeneous and non-isotropic porous media with full tensor diffusion coefficients, which is a common situation associated with the miscible displacement of contaminants in aquifers and the immiscible and incompressible two-phase flow of oil and water in petroleum reservoirs, involves the numerical solution of an elliptic type equation in which the diffusion coefficient can be discontinuous, varying orders of magnitude within short distances. In the present work, we present a vertex-centered edge-based finite volume method (EBFV) with median dual control volumes built over a primal mesh. This formulation is capable of handling the heterogeneous and anisotropic media using structured or unstructured, triangular or quadrilateral meshes. In the EBFV method, the discretization of the diffusion term is performed using a node-centered discretization implemented in two loops over the edges of the primary mesh. This formulation guarantees local conservation for problems with discontinuous coefficients, keeping second-order accuracy for smooth solutions on general triangular and orthogonal quadrilateral meshes. In order to show the convergence behavior of the proposed EBFV procedure, we solve three benchmark problems including full tensor, material heterogeneity and distributed source terms. For these three examples, numerical results compare favorably with others found in literature. A fourth problem, with highly non-smooth solution, has been included showing that the EBFV needs further improvement to formally guarantee monotonic solutions in such cases. Copyright © 2008 John Wiley & Sons, Ltd. [source]


Kinetic study of the manganese-based catalytic hydrogen peroxide oxidation of a persistent azo-dye

JOURNAL OF CHEMICAL TECHNOLOGY & BIOTECHNOLOGY, Issue 2 2010
Chedly Tizaoui
Abstract BACKGROUND: The discharge of synthetic dyes by the textile industry into the environment poses concerns due to their persistence and toxicity. New efficient treatment processes are required to effectively degrade these dyes. The aim of this work was to study the degradation of a persistent dye (Drimarene Brilliant Reactive Red K-4BL, C.I.147) using H2O2 oxidation catalysed by an Mn(III)-saltren catalyst and to develop a kinetic model for this system. RESULTS: Dye oxidation with H2O2 was significantly improved by the addition of the catalyst. As the pH was increased from 3 to 10, the oxidation rates increased significantly. The kinetic model developed in this study was found to adequately explain the experimental results. In particular, dye oxidation can be described at high pH by pseudo-first-order kinetics. A Michaelis,Menton type equation was developed from the model and was found to adequately describe the effect of H2O2 and catalyst concentrations on the apparent pseudo-first-order rate constant. Optimum catalyst and H2O2 concentrations of 500 mg L,1 and 6.3 g L,1, respectively, were found to give maximum reaction rates. CONCLUSION: Catalytic H2O2 oxidation was found to be effective for the removal of persistent dye and the results obtained in this work are of significance for design and scale-up of a treatment process. Copyright © 2009 Society of Chemical Industry [source]


A Cahn,Hilliard type equation with periodic gradient-dependent potentials and sources

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 3 2010
Yinghua Li
Abstract This paper is concerned with the existence, uniqueness and attractability of time periodic solutions of a Cahn,Hilliard type equation with periodic gradient-dependent potentials and sources. Copyright © 2009 John Wiley & Sons, Ltd. [source]


Stability of global and exponential attractors for a three-dimensional conserved phase-field system with memory

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 18 2009
Gianluca Mola
Abstract We consider a conserved phase-field system on a tri-dimensional bounded domain. The heat conduction is characterized by memory effects depending on the past history of the (relative) temperature ,, which is represented through a convolution integral whose relaxation kernel k is a summable and decreasing function. Therefore, the system consists of a linear integrodifferential equation for ,, which is coupled with a viscous Cahn,Hilliard type equation governing the order parameter ,. The latter equation contains a nonmonotone nonlinearity , and the viscosity effects are taken into account by a term ,,,,t,, for some ,,0. Rescaling the kernel k with a relaxation time ,>0, we formulate a Cauchy,Neumann problem depending on , and ,. Assuming a suitable decay of k, we prove the existence of a family of exponential attractors {,,,,} for our problem, whose basin of attraction can be extended to the whole phase,space in the viscous case (i.e. when ,>0). Moreover, we prove that the symmetric Hausdorff distance of ,,,, from a proper lifting of ,,,0 tends to 0 in an explicitly controlled way, for any fixed ,,0. In addition, the upper semicontinuity of the family of global attractors {,,,,,} as ,,0 is achieved for any fixed ,>0. Copyright © 2009 John Wiley & Sons, Ltd. [source]


Best Sobolev constants and quasi-linear elliptic equations with critical growth on spheres

MATHEMATISCHE NACHRICHTEN, Issue 12-13 2005
C. Bandle
Abstract Sharp existence and nonexistence results for positive solutions of quasilinear elliptic equations with critical growth in geodesic balls on spheres are established. The arguments are based on Pohozaev type identities and asymptotic estimates for Emden,Fowler type equations. By means of spherical symmetrization and the concentration-compactness principle existence and nonexistence results for general domains on spheres are obtained. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]


Can error source terms in forecasting models be represented as Gaussian Markov noises?

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 609 2005
C. Nicolis
Abstract The repercussions of model error on the long term climatological means and on the variability around them are analysed. The extent to which a stochastic representation of error source terms provides a universal correcting mechanism is addressed. General relations are derived linking the model error to the climatological means and the variability properties of a forecasting model subjected to a correcting Gaussian Markov noise on the basis of moment equations associated with Fokker,Planck and Liouville type equations. These relations are implemented in a variety of models giving rise to regular and to chaotic solutions. As it turns out, forecasting models fall into distinct universality classes differing in their response to the effect of noise according to the structure of the Jacobian and the Hessian matrices of the model phase-space velocity. It is concluded that different trends may exist in which the ,correcting' noise tends to depress or, on the contrary, amplify the model error. Copyright © 2005 Royal Meteorological Society. [source]


Weakly nonlocal irreversible thermodynamics

ANNALEN DER PHYSIK, Issue 3 2003
P. Ván
Abstract Weakly nonlocal thermodynamic theories are critically revisited. A relocalized, irreversible thermodynamic theory of nonlocal phenomena is given, based on a modified form of the entropy current and new kind of internal variables, the so called current multipliers. The treatment is restricted to deal with nonlocality connected to dynamic thermodynamic variables. Several classical equations are derived, including Guyer-Krumhansl, Ginzburg-Landau and Cahn-Hilliard type equations. [source]