Numerical Simulations for Saltwater Intrusion by the Mixed Hybrid Finite Element Method and Discontinuous Finite Element Method

The proposed numerical code simulates the displacement of two miscible fluids through a saturated porous medium (2D configuration). Coupling between flow and transport is carried out by an equation of state. In the mixing zone, the density is assumed to vary as a function of concentration. The model uses a combination of the mixed hybrid finite element method and the discontinuous finite element method.Applied in its classical development, the mixed hybrid finite element method leads to a non-conservative formulation of the mass balance equation. However, one of the main reasons for using this technique is the ability to conserve mass cell-by-cell. Consequently, a new formulation that makes it possible to hold the conservative form of the continuity equation and so preserve the mass cell-wise is proposed. Although the pertinence of these approaches could have also been tested on other standard benchmarks, e.g., Elder's problem or salt dome problem, we have voluntarily limited ourselves to Henry's problem (1964). This choice was dictated by the possibility of a comparison with a semi-analytical solution. Contrary to previous numerical results, the comparison is made for the whole mixing zone. The very good agreement between our results and the semi-analytical solution shows the robustness and the efficiency of this approach for the seawater intrusion problems.     

Adaptive finite elements with large aspect ratio for mass transport in electroosmosis and pressure‐driven microflows

A space–time adaptive method is presented for the numerical simulation of mass transport in electroosmotic and pressure‐driven microflows in two space dimensions. The method uses finite elements with large aspect ratio, which allows the electroosmotic flow and the mass transport to be solved accurately despite the presence of strong boundary layers. The unknowns are the external electric potential, the electrical double layer potential, the velocity field and the sample concentration. Continuous piecewise linear stabilized finite elements with large aspect ratio and the Crank–Nicolson scheme are used for the space and time discretization of the concentration equation. Numerical results are presented showing the efficiency of this approach, first in a straight channel, then in crossing and multiple T‐form configuration channels. Copyright © 2009 John Wiley & Sons, Ltd.     

Pseudostress–velocity formulation for incompressible Navier–Stokes equations

This paper presents a numerical algorithm using the pseudostress–velocity formulation to solve incompressible Newtonian flows. The pseudostress–velocity formulation is a variation of the stress–velocity formulation, which does not require symmetric tensor spaces in the finite element discretization. Hence its discretization is greatly simplified. The discrete system is further decoupled into an H ( div ) problem for the pseudostress and a post‐process resolving the velocity. This can be done conveniently by using the penalty method for steady‐state flows or by using the time discretization for nonsteady‐state flows. We apply this formulation to the 2D lid‐driven cavity problem and study its grid convergence rate. Also, computational results of the time‐dependent‐driven cavity problem and the flow past rectangular problem are reported. Copyright © 2009 John Wiley & Sons, Ltd.     

Augmented Lagrangian-based preconditioners for steady buoyancy driven flow

In this paper, we apply the augmented Lagrangian (AL) approach to steady buoyancy driven flow problems. Two AL preconditioners are developed based on the variable’s order, specifically whether the leading variable is the velocity or the temperature variable. Correspondingly, two non-augmented Lagrangian (NAL) preconditioners are also considered for comparison. An eigenvalue analysis for these two pairs of preconditioners is conducted to predict the rate of convergence for the GMRES solver. The numerical results show that the AL preconditioner pair is insensitive with respect to the mesh size, Rayleigh number, and Prandtl number in terms of GMRES iterations, resulting in a significantly more robust preconditioner pair compared to the NAL pair. Accordingly, the AL pair performs much better than the NAL pair in terms of computational time. For the AL pair, the preconditioner with velocity as the leading variable gives slightly better efficiency than the one with temperature as the leading variable.     

Potentials of mean force for hydrophobic interactions between hydrocarbons in water solution: dependence on temperature,solute shape,and solute size

We carried out molecular dynamics (MD) simulations with the AMBER force field for four pairs of spherical dimers of different size (neopentane, bicyclooctane, adamantane, and fullerene‐C₆₀) using the TIP3P model of water as solvent. For comparison, we performed MD simulations for a linear molecule of n‐pentane at the same conditions. To assess the entropy contribution to the Gibbs free energy, MD simulations were run at three different temperatures of 273 K, 323 K, and 348 K, respectively, using umbrella‐sampling/the WHAM method. The stability of dimers is described by a potential of mean force (PMF). The shape of PMF curves for hydrophobic interactions is characteristic, and entails a contact minimum, a solvent‐separated minimum, and a desolvation maximum. The depth and position of the contact minimum for each pair change with the size of the nonpolar particle, and are consequently shifted to a larger distance for larger molecules. Additionally, the Lennard–Jones contribution to the PMF increases simultaneously with an increase in particle size. For a linear dimer, the contact minimum is shifted to a shorter distance than it is for spherical systems with the same number of carbon atoms. The contact minima on PMF curves increase with temperature, suggesting that the association entropy is positive. Dimensionless PMF curves showed a low dependency (near contact minima regions) on temperature, as the association entropy is low. Copyright © 2014 John Wiley & Sons, Ltd.     

A Small Noise Asymptotic Expansion for Young SDE Driven by Fractional Brownian Motion: A Sharp Error Estimate With Malliavin Calculus

This article shows an analytically tractable small noise asymptotic expansion with a sharp error estimate for the expectation of the solution to Young’s pathwise stochastic differential equations (SDEs) driven by fractional Brownian motions with the Hurst index H > 1/2. In particular, our asymptotic expansion can be regarded as small noise and small time asymptotics by the error estimate with Malliavin culculus. As an application, we give an expansion formula in one-dimensional general Young SDE driven by fractional Brownian motion. We show the validity of the expansion through numerical experiments.     

k‐Version of finite element method in 2‐D polymer flows: Oldroyd‐B constitutive model

In this paper, a new mathematical framework based on h, p, k and variational consistency (VC) of the integral forms is utilized to develop a finite element computational process of two‐dimensional polymer flows utilizing Oldroyd‐B constitutive model. Alternate forms of the choices of dependent variables in the governing differential equations (GDEs) are considered and is concluded that u, v, p, τ choice yielding strong form of the GDEs is meritorious over others. It is shown that: (a) since, the differential operator in the GDEs is non‐linear, Galerkin method and Galerkin method with weak form are variationally inconsistent (VIC). The coefficient matrices in these processes are non‐symmetric and hence may have partial or completely complex basis and thus the resulting computational processes may be spurious. (b) Since the VC of the VIC integral forms cannot be restored through any mathematically justifiable means, the computational processes in these approaches always have possibility of spurious solutions. (c) Least squares process utilizing GDEs in u, v, p, τ (strong form of the GDEs) variables (as well as others) is variationally consistent. The coefficient matrices are always symmetric and positive definite and hence always have a real basis and thus naturally yield computational processes that are free of spurious solutions. (d) The theoretical solution of the GDEs are generally of higher order global differentiability. Numerical simulations of such solutions in which higher order global differentiability characteristics of the theoretical solution are preserved, undoubtedly requires local approximations in higher order scalar product spaces . (e) LSP with local approximations in spaces provide an incomparable mathematical and computational framework in which it is possible to preserve desired characteristics of the theoretical solution in the computational process. Numerical studies are presented for fully developed flow between parallel plates and a lid driven square cavity. M1 fluid is used in all numerical studies. The range of applicability of the Oldroyd‐B model or lack of it is examined for both model problems for increasing De. A mathematical idealization of the corners where stationary wall meets the lid is presented and is shown to simulate the real physics when the local approximations are in higher order spaces and when h_d→0. For both model problems shear rate is examined in the flow domain to establish validity of the Oldroyd‐B constitutive model. Copyright © 2006 John Wiley & Sons, Ltd.     

多协议标记交换——多媒体远程教育IP网络的核心技术

对多协议标记交换（Ｍｕｌｔｉ－ＰｒｏｔｏｃｏｌＬａｂｅｌＳｗ ｉｔｃｈｉｎｇ,ＭＰＬＳ）的基本概念及其工作原理进行了介绍,随后对它的关键技术进行了分析,最后对几个相关的问题进行了讨论．     

Field Theory of Critical Behavior in Driven Diffusive Systems with Quenched Disorder

We present a field-theoretic renormalization-group study for the critical behavior of a uniformly driven diffusive system with quenched disorder, which is modeled by different kinds of potential barriers between sites. Due to their symmetry properties, these different realizations of the random potential barriers lead to three different models for the phase transition to transverse order and to one model for the phase transition to longitudinal order all belonging to distinct universality classes. In these four models, which have different upper critical dimensions d _c, we find the critical scaling behavior of the vertex functions in spatial dimensions d<d _c. The deviation from purely diffusive behavior is characterized by the anomaly exponent , which we calculate at first and second order, respectively, in =d _c–d. In each model turns out to be positive, which means superdiffusive spread of density fluctuations in the driving force direction.