Global existence of strong solutions to a time‐dependent 3D Ginzburg‐Landau model for superconductivity with partial viscous terms

We study an initial boundary value problem for a time‐dependent 3D Ginzburg‐Landau model of superconductivity with partial viscous terms. We prove the global existence of strong solutions.     

SERIES PERTURBATIONS APPROXIMATE SOLUTIONS TO N-S EQUATIONS AND MODIFICATION TO ASYMPTOTIC EXPANSION MATCHED METHOD

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Local discontinuous Galerkin method for a nonlocal viscous conservation laws

The purpose of this article is to investigate high‐order numerical approximations of scalar conservation laws with nonlocal viscous term. The viscous term is given in the form of convolution in space variable. With the help of the characteristic of viscous term, we design a semidiscrete local discontinuous Galerkin (LDG) method to solve the nonlocal model. We prove stability and convergence of semidiscrete LDG method in L² norm. The theoretical analysis reveals that the present numerical scheme is stable with optimal convergence order for the linear case, and it is stable with sub‐optimal convergence order for nonlinear case. To demonstrate the validity and accuracy of our scheme, we test the Burgers equation with two typical nonlocal fractional viscous terms. The numerical results show the convergence order accuracy in space for both linear and nonlinear cases. Some numerical simulations are provided to show the robustness and effectiveness of the present numerical scheme.     

The improvement of numerical modeling in the solution of incompressible viscous flow problems using finite element method based on spherical Hankel shape functions

In this paper, the finite element method with new spherical Hankel shape functions is developed for simulating 2‐dimensional incompressible viscous fluid problems. In order to approximate the hydrodynamic variables, the finite element method based on new shape functions is reformulated. The governing equations are the Navier‐Stokes equations solved by the finite element method with the classic Lagrange and spherical Hankel shape functions. The new shape functions are derived using the first and second kinds of Bessel functions. In addition, these functions have properties such as piecewise continuity. For the enrichment of Hankel radial basis functions, polynomial terms are added to the functional expansion that only employs spherical Hankel radial basis functions in the approximation. In addition, the participation of spherical Bessel function fields has enhanced the robustness and efficiency of the interpolation. To demonstrate the efficiency and accuracy of these shape functions, 4 benchmark tests in fluid mechanics are considered. Then, the present model results are compared with the classic finite element results and available analytical and numerical solutions. The results show that the proposed method, even with less number of elements, is more accurate than the classic finite element method.     

Study of Viscosity-temperature Properties of Oil and Gas-condensate Mixtures in Critical Temperature Ranges of Phase Transitions

Transport of oil and gas-condensate mixtures of various compositions is found to be accompanied by a slight increase in viscosity in the coldest period when ground temperatures at depth of a condensate pipeline reach 0 – minus 4°С. Fall in temperature of oil fluids under study to minus 10 – minus 30°С is accompanied by a sharp increase in all structural and rheological parameters of the mixture. Even a slight amount of oil added to a gas-condensate mixture causes a significant decrease in viscosity in the negative temperature range. As a result, cloud and pour point of a mixture falls, its amount decreases, the structure of paraffin deposits changes.     

Enzyme immobilization strategies for the design of robust and efficient biocatalysts

Different strategies for the preparation of efficient and robust immobilized biocatalysts are here reviewed. Different physico-chemical approaches are discussed.i.- The stabilization of enzyme by any kind of immobilization on pre-existing porous supports.ii.- The stabilization of enzymes by multipoint covalent attachment on support surfaces.iii.- Additional stabilization of immobilized-stabilized enzyme by physical or chemical modification with polymers.These three strategies can be easily developed when enzymes are immobilized in pre-existing porous supports. In addition to that, these immobilized-stabilized derivatives are optimal to develop enzyme reaction engineering and reactor engineering. Stabilizations ranging between 1000 and 100,000 folds regarding diluted soluble enzymes are here reported.     

Boundary Layer Flow over a Curved Surface Imbedded in Porous Medium

This research is made to visualize the boundary layer flow by a curved stretching sheet embedded in porous medium. The geometry is bended(curved), therefore the curvilinear coordinates are used to model the present problem.Fluid is electrically conducting with the presence of uniform magnetic field. The governing non-linear partial differential equation reduces to non-linear ordinary differential equations by using the dimensionless suitable transformations. The numerical solutions are obtained by using the method bvp4c from MATLAB. The effects of curvature parameter, nondimensional magnetic parameter, and porosity parameter on the velocity field and skin friction coefficient are examined.The skin friction profile enhances with enhancing the values of porosity and magnetic parameter. Comparison of the present results with the existing results in the literature for the flat surface is also given.     

An embedded boundary framework for compressible turbulent flow and fluid–structure computations on structured and unstructured grids

The finite volume method with exact two‐phase Riemann problems (FIVER) is a two‐faceted computational method for compressible multi‐material (fluid–fluid, fluid–structure, and multi‐fluid–structure) problems characterized by large density jumps, and/or highly nonlinear structural motions and deformations. For compressible multi‐phase flow problems, FIVER is a Godunov‐type discretization scheme characterized by the construction and solution at the material interfaces of local, exact, two‐phase Riemann problems. For compressible fluid–structure interaction (FSI) problems, it is an embedded boundary method for computational fluid dynamics (CFD) capable of handling large structural deformations and topological changes. Originally developed for inviscid multi‐material computations on nonbody‐fitted structured and unstructured grids, FIVER is extended in this paper to laminar and turbulent viscous flow and FSI problems. To this effect, it is equipped with carefully designed extrapolation schemes for populating the ghost fluid values needed for the construction, in the vicinity of the fluid–structure interface, of second‐order spatial approximations of the viscous fluxes and source terms associated with Reynolds averaged Navier–Stokes (RANS)‐based turbulence models and large eddy simulation (LES). Two support algorithms, which pertain to the application of any embedded boundary method for CFD to the robust, accurate, and fast solution of FSI problems, are also presented in this paper. The first one focuses on the fast computation of the time‐dependent distance to the wall because it is required by many RANS‐based turbulence models. The second algorithm addresses the robust and accurate computation of the flow‐induced forces and moments on embedded discrete surfaces, and their finite element representations when these surfaces are flexible. Equipped with these two auxiliary algorithms, the extension of FIVER to viscous flow and FSI problems is first verified with the LES of a turbulent flow past an immobile prolate spheroid, and the computation of a series of unsteady laminar flows past two counter‐rotating cylinders. Then, its potential for the solution of complex, turbulent, and flexible FSI problems is also demonstrated with the simulation, using the Spalart–Allmaras turbulence model, of the vertical tail buffeting of an F/A‐18 aircraft configuration and the comparison of the obtained numerical results with flight test data. Copyright © 2014 John Wiley & Sons, Ltd.     

On the Capillary Coupling between Two Phases in a Droplet Train Model

A droplet train model proposed by Foulser {\it et al.} ({\it Transport in Porous Media} (1991), 223) is modified with addition of capillary resistance. It is shown that linear transport equations for this model can be represented in the Onsager form, where the generalized thermodynamic forces are pressure gradients of corresponding phases. In particular, the onset of capillary interactions give rise to the nonzero and equal cross term coefficients.     

The Gibbs Energies of Activation of Lysozyme for Viscous Flow in Water + Dimethyl Sulfoxide Solutions at 298.15 K

Gibbs energies of activation for viscous flow of binary water (1) + dimethyl sulfoxide (2) mixtures, Δμ ₁₂^○, and of lysozyme (3) in corresponding ternary mixtures, Δμ ₃^○, were determined at 298.15 K. The binary mixtures have a maximum in the value of the excess quantity for Δμ ₁₂^○ at a dimethyl sulfoxide mole fraction of x ₂≈0.31. The values of Δμ ₃^○ are larger than Δμ ₁₂^○ at all values of x ₂, even when normalized by their molar volumes, suggesting that the solvents interact more strongly with lysozyme than with themselves. The values of Δμ ₃^○ significantly increased in the range of x ₂=0.3 to 0.4 because of an increase in solvent-lysozyme interactions, which resulted from an increase in the accessible surface area of lysozyme that was exposed by its unfolding. The mean value obtained for Δμ ₃^○ per amino acid of lysozyme at x ₂=0.2 is greater than that for hydrophobic amino acids, indicating that the solvent interacts with hydrophilic amino acids more strongly than with hydrophobic ones.