Some A Priori Bounds for Flows through Heterogeneous Media

Under various conditions, analytical bounds on important displacementcharacteristics are derived for incompressible flows throughheterogeneous rectangular regions. They rely on bounds on theintermediate-scale Darcy permeability and also on its rate ofvariation with position, and can be calculated prior to fieldor laboratory displacement tests. It is suggested that thesebounds can be used in a probabilistic manner. Their limitations,applications, and possible extensions are discussed.     

Robust Multiscale Iterative Solvers for Nonlinear Flows in Highly Heterogeneous Media

In this paper, we study robust iterative solvers for finite element systems resulting in approximation of steady-state Richards' equation in porous media with highly heterogeneous conductivity fields. It is known that in such cases the contrast, ratio between the highest and lowest values of the conductivity, can adversely affect the performance of the preconditioners and, consequently, a design of robust preconditioners is important for many practical applications. The proposed iterative solvers consist of two kinds of iterations, outer and inner iterations. Outer iterations are designed to handle nonlinearities by linearizing the equation around the previous solution state. As a result of the linearization, a large-scale linear system needs to be solved. This linear system is solved iteratively (called inner iterations), and since it can have large variations in the coefficients, a robust preconditioner is needed. First, we show that under some assumptions the number of outer iterations is independent of the contrast. Second, based on the recently developed iterative methods, we construct a class of preconditioners that yields convergence rate that is independent of the contrast. Thus, the proposed iterative solvers are optimal with respect to the large variation in the physical parameters. Since the same preconditioner can be reused in every outer iteration, this provides an additional computational savings in the overall solution process. Numerical tests are presented to confirm the theoretical results.     

Monotone Mappings and Flows of Viscous Media

We establish solvability of the boundary-value problems describing stationary and periodic flows of viscoplastic media. In the case of stationary flows we study the question of convergence of the Galerkin method. For the problem of periodic flows we prove a version of the second Bogolyubov theorem.     

平衡规划问题的熵函数方法及其在混合交通流中的应用

将参变极值问题的极大熵函数方法应用到求解平衡规划问题中,通过先验分布信息和Kullback熵概念,给出了平衡规划问题基于Kullback熵表示的熵函数求解方法,并将平衡规划的极大熵函数方法应用于求解混合交通平衡分配问题．     

Updating Network Flows Given Multiple,Heterogeneous Arc Attribute Changes

A dual ascent reoptimization technique is proposed for updating optimal flows for the minimum cost network flow problem (MCNFP) given any number of simultaneous, heterogeneous changes to the network attributes (i.e. supply at nodes, arc costs and arc capacities) and the optimal solutions to the prior primal and dual problems. Significant savings in computation time can be achieved through the use of reoptimization in place of solving a new MCNFP from scratch as each new problem instance (i.e. set of network attribute updates) arises. The proposed technique can be implemented with polynomial worst-case computational complexity. Extensive numerical experiments were designed and conducted to assess the computational benefits of employing the proposed reoptimization technique as compared with solution from scratch using comparable classic implementations of the original algorithms. This work was motivated by the need for the real-time provision of evacuation instructions to people seeking quick egress from a large sensor-equipped building that has come under attack by natural or terrorist forces, but has broad applicability.     

Dynamics of a Reaction-diffusion-ODE System in a Heterogeneous Media

The existence and stability of stationary solutions for a reaction-diffusion-ODE system are investigated in this paper. We first show that there exist both continuous and discontinuous stationary solutions.Then a good understanding of the stability of discontinuous stationary solutions is gained under an appropriate condition. In addition, we demonstrate the influences of the diffusion coefficient on stationary solutions. The results we obtained are based on the super-/sub-solution method and the generalized mountain pass theorem.Finally, some numerical simulations are given to illustrate the theoretical results.     

Mixed Method for Compressible Miscible Displacement with Dispersion in Porous Media

Compressible miscible displacement of one fluid by another in porous media is modelled by a nonlinear parabolic system. A finite element procedure is introduced to approximate the concentration of one fluid and the pressure of the mixture. The concentration is treated by a Galerkin method while the pressure is treated by a parabolic mixed finite element method. The effect of dispersion, which is neglected in [1], is considered. Optimal order estimates in L2 are derived for the errors in the approximate solutions.     

Numerical Simulation of Two-Phase Flow through Heterogeneous Porous Media

A mixed finite element method is combined to finite volume schemes on structured and unstructured grids for the approximation of the solution of incompressible flow in heterogeneous porous media. A series of numerical examples demonstrates the effectiveness of the methodology for a coupled system which includes an elliptic equation and a nonlinear degenerate diffusion–convection equation arising in modeling of flow and transport in porous media.     

Thermodynamics and Optimal Control of Porous Media Flows in Oil Field Development

The nonisothermal two-phase porous media flow of oil and hot water in a horizontal oil reservoir is considered. An asymptotic method for calculating the flow and solving related optimal control problems is proposed. Namely, the problem of choosing optimal control actions to maximize the oil production for a given level of financial costs and to minimize the costs for a given level of oil production is considered.     

A Method for Numerical Simulation of Haline Convective Flows in Porous Media as Applied to Geology

Computational Mathematics and Mathematical Physics - A numerical code for simulating haline convective flows in porous media based on the finite difference method on a staggered nonuniform grid is...     

Adaptive Mesh Refinement Simulations of Gas Dynamic Flows on Hybrid Meshes

Doklady Mathematics - An adaptive mesh refinement algorithm for simulations of the Navier–Stokes equations on unstructured hybrid meshes is presented. Numerical results for compressible...     

ADAPT: An Adaptive Approach to Media Decisions

A firm's market changes under the impact of the firm's advertising. Feedback information on the market response allows the firm to learn about such changes and to adapt its subsequent media decisions accordingly. This paper presents an adaptive media model (ADAPT) that utilizes feedback information to revise certain parameters in a media decision model. Simulation experiments conducted with the ADAPT model demonstrate how different types of feedback information affect the media decisions and thereby the expected net profit contributions from sales. It is shown how the economic value of feedback information depends on the characteristics of the firm's market and also on the revision rules applied for updating the parameters. The value of the information may actually be negative if it is not used "intelligently".     

Convergence of Weak Galerkin Finite Element Method for Second Order Linear Wave Equation in Heterogeneous Media

Weak Galerkin finite element method is introduced for solving wave equation with interface on weak Galerkin finite element space $(\mathcal{P}_k(K), \mathcal{P}_{k−1}(∂K), [\mathcal{P}_{k−1}(K)]^2).$ Optimal order a priori error estimates for both space-discrete scheme and implicit fully discrete scheme are derived in $L^∞(L^2)$ norm. This method uses totally discontinuous functions in approximation space and allows the usage of finite element partitions consisting of general polygonal meshes. Finite element algorithm presented here can contribute to a variety of hyperbolic problems where physical domain consists of heterogeneous media.     

Adaptive Finite–Element Procedures for Homogenization Analysis of Heterogeneous Micro–Structures

The paper investigates adaptive finite element procedures for the treatment of homogenize macro‐continuums with locally attached micro‐structures of nonlinear elastic and elastoplastic constituents. The deformation of the microstructure is assumed to be driven by a macroscopic strain mode. In this context we investigate different constraints for the fluctuation field base on variational formulations. For the computation of the overall response of the microstructures we develop a distinct adaptive finite element procedure. We consider possible a priori and a posteriori error estimators for the homogenization analysis in connection with an adaptive remeshing procedure.     

Modulation Equations of Weakly Nonlinear Geometrical Optics in Media Exhibiting Mixed Nonlinearity

The system of evolutionary equations describing the asymptotic behavior of nonlinear waves propagating in materials exhibiting mixed nonlinearity is derived with the resonant wave interactions inherent in the system. Our analysis differs from the results of Hunter et al., in that we have employed a different scaling, keeping in view the delayed effects of nonlinearity in certain thermodynamic systems exhibiting mixed nonlinearity. The result is to modify the transport equations obtained by Hunter et al. by the addition of certain cubic nonlinear terms. Through the method of averaging, the secular terms are eliminated. However, the averaging process is carried out in two steps; first, along manifolds of codimension two giving an advection equation, the solution of which is then averaged in a direction transverse to the above-mentioned manifold.     

基于动态自适应t分布变异的人群搜索算法

针对人群搜索算法在进化后期大量个体聚集局部最优时,易陷入局部最优,搜索精度低的缺陷,提出一种基于t分布变异的人群搜索算法.算法使用动态自适应方式确定变异步长,引入t分布变异算子以融合柯西变异和高斯变异的优点,促进算法在进化早期具备良好的全局探索能力,在进化后期收获较强的局部开发能力,增加种群的多样性;采用边界缓冲墙策略处理越界问题,避免越界个体聚集在边界值上的缺陷.实验结果表明,算法比基本人群搜索算法具有更高的寻优精度和收敛速度,是一种有效的算法.