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.     

粘性流体间夹有多孔介质时的非定常流动及其热传导

粘性流体间夹有多孔介质,流经壁面温度等温的水平管道时,研究其非定常振荡流动及其热传导问题.多孔介质中的流动采用Brinkman方程模型.通过集中非周期项和周期项,将偏微分的控制方程转化为常微分方程,并利用边界和界面条件,找到了每个区间的闭式解.数值计算了各种物理参数,如多孔性参数、频率参数、周期频率参数、粘度比、热传导系数比和Prandtl数,对速度和温度场的影响,并给出相应的图形.此外,导出了壁顶和壁底处的热传递率并用表格列出.     

热交换多孔圆盘间三阶流体的MHD轴对称流动

在两个具有热交换可渗透的多孔圆盘之间,研究三阶流体的磁流体动力学(MHD)流动.通过适当变换,将偏微分的控制方程转换为常微分方程.采用同伦分析法(HAM)求解转换后的方程.定义了均方残余误差的表达式,并选择了最佳的、收敛的控制参数值.检测了无量纲参数变化时的无量纲速度和温度场.列表显示表面摩擦因数和Nusselt数,并分析了无量纲参数的影响.     

A Note on Laminar Flow through a Porous Pipe with Slip

An analytic solution is developed for flow through a porouspipe when slip occurs. The solution should be useful in a rangeof problems in fluids engineering and chemical engineering.     

流过多孔介质的流体研究

研究流过密集的具二次变化渗透性的重叠理想聚合体的流体．流体流由达西定律的布林克曼扩展及连续方程来刻画,通过引入流函数,求出上述方程在适当边界条件下的解析解,并将结果与一些已知的结果进行了比较．     

On the Potential Flow of an Ideal Incompressible Fluid through a Porous Boundary

The potential flow of an incompressible fluid is considered.The fluid is supposed to be ideal except on the porous boundarywhere the normal velocity is proportional to the pressure. Thisleads to the Laplace equation with the square of the gradientin the boundary condition. The linearized problem (small velocities)is trivially solvable by the variational method in the usualenergy space. The nonlinearity of the boundary condition beingtoo strong for that space, the stationary problem is treatedin some Banach algebras of functions defined on the boundaryof . The existence and uniqueness of the solution are provedfor small flows or for large boundary resistances.     

流经有热源多孔平板并伴有化学反应的传热传质混合对流MHD流动

对流经无限竖直多孔平板的不可压缩粘性导电流体,稳定的传热传质混合对流MHD流动问题,给出了精确解和数值解.假定均匀磁场横向作用于流动方向,考虑了感应磁场及其能量的粘性和磁性损耗.多孔平板有恒定的吸入速度并均匀地混入流动速度.用摄动技术和数值方法求解控制方程.得到了平板上速度场、温度场、感应磁场、表面摩擦力和传热率的分析表达式.相关参数取不同数值时,用图形表示出问题的数值结果.讨论了从平板到流体的Hartmann数、化学反应参数、磁场的Prandtl数,以及包括速度场、温度场、浓度场和感应磁场等其它参数的影响.可以发现,热源/汇或Eckert数的增大,极大地提高了流体的速度值.x-方向的感应磁场随着Hartmann数、磁场的Prandtl数、热源/汇和粘性耗散的增大而增大.但是,研究表明,随着破坏性化学反应(K0)的增大,流动速度、流体温度和感应磁场将减小.对色谱分析系统和材料加工的磁场控制,该研究在热离子反应堆模型、电磁感应、磁流体动力学传输现象中得到了应用.     

热辐射对粘性流体流过多孔非线性收缩平面时的MHD流动和热传导的影响

研究热辐射对多孔非线性收缩平面上磁流体动力学(MHD)流动和热传导的影响.假设收缩平面的速度和横向磁场,按离原点距离的幂函数而变化;又假设粘性按与其有关的温度的反函数变化,热传导率按温度的线性函数变化.通过广义相似变换,将偏微分方程的控制方程,简化为耦合的非线性常微分方程,然后通过有限差分法进行数值求解.在不同的参数取值下,得到速度和温度分布,以及多孔平面上表面摩擦因数和热传导率的数值结果.     

Study of a Numerical Approach for a Transient Flow Problem in Porous Media

In this work, we deal with the numerical study of the new approximation method proposed in [7] for a transient flow problem in porous media. The stationary problem, obtained from a time discretization of this transient problem, is considered as an optimal shape design formulation. We prove the existence of the solution of the discrete optimal shape problem obtained from finite element discretization. We study the convergence and give numerical results showing the efficiency of the proposed approach.     

Heat Flow from Polygons

Potential Analysis - We study the heat flow from an open, bounded set D in $mathbb {R}^{2}$ with a polygonal boundary ?D. The initial condition is the indicator function of D. A Dirichlet 0...     

放/吸热流体在两个充满多孔材料的竖直平行板之间作不稳定的自然对流

在一个由两块无限竖直平行板组成的管道中,充满着多孔的介质材料,使用Darcy模型(Brinkman模型的推广)的动量方程,连同能量方程,计算不可压缩、粘性、放/吸热流体在该管道中的不稳定自然对流,即Couette流动.流动是由于边界平板有不对称的加热,以及作加速运动所引起.选用合理的无量纲参数,对控制方程进行简化,通过Laplace变换进行解析求解,得到闭式的速度和温度分布曲线解,随后导出表面摩擦力和传热率.发现在竖直管道中的不同剖面,流体的流动及温度分布曲线随着时间而增加,且在运动平板附近更高.特别是,流体的速度和温度随着平板间距的增加而增加,但是,表面摩擦力和热传导率随着平板间距的增加而减小.     

Liquid Flow in Partially Saturated Porous Media

We consider a picture for the filtration of a liquid in a partiallysaturated porous medium, leading to a two-phase one-dimensionalfree boundary problem of the following type: The liquid pressuresatisfies an elliptic equation in the saturated region and anon-linear parabolic equation in the unsaturated region, whilepressure and velocity are continuous across the interface. This scheme reduces to the study of the non-linear parabolicfree boundary problem in the unsaturated phase with cauchy dataprescribed on the free boundary, for such a problem existence,uniqueness and continuous dependence theorems are proved.     

Two-Component Two-Compressible Flow in a Porous Medium

We prove existence of solutions of a two-compressible (liquid and gas) phase flow model in porous media with two components (water and hydrogen). This model is obtained by writing the mass conservation for each component in each phase. We suppose that the mass exchange between dissolved hydrogen and hydrogen in the gas phase is supposed finite. This mass exchange is modeled by a source term on each mass conservation equations.     

Unsteady Porous Flow with a Free Surface

Three different numerical methods for solving unsteady two-dimensionalporous flow problems with a free surface are presented. Thevelocity potential is expressed as the solution to a variationalproblem which is solved by a Rayleigh-Ritz expansion, a Kantorovichexpansion and a co-ordinate transformation method. The freesurface equation is solved by a Crank-Nicolson procedure. Thethree methods were tested on the same set of problems and theobtained results are virtually identical.     

Floer Homology and the Heat Flow

We study the heat flow in the loop space of a closed Riemannian manifold M as an adiabatic limit of the Floer equations in the cotangent bundle. Our main application is a proof that the Floer homology of the cotangent bundle, for the Hamiltonian function kinetic plus potential energy, is naturally isomorphic to the homology of the loop space. J.W. received partial financial support from TH-Projekt 00321. Received: December 2004 Revision: September 2005 Accepted: September 2005     

The Heat Flow of the CCR Algebra

Let Pf(x) = –if'(x) and Qf(x) = xf(x) be the canonicaloperators acting on an appropriate common dense domain in L²(R).The derivations D_P(A) = i(PA–AP) and D_Q(A) = i(QA–AQ)act on the *-algebra A of all integral operators having smoothkernels of compact support, for example, and one may considerthe noncommutative ‘Laplacian’, L = + , as a linear mapping of A into itself. L generates a semigroup of normal completely positive linearmaps on B(L₂(R)), and this paper establishes some basic propertiesof this semigroup and its minimal dilation to an E₀-semigroup.In particular, the author shows that its minimal dilation ispure and has no normal invariant states, and he discusses thesignificance of those facts for the interaction theory introducedin a previous paper. There are similar results for the canonical commutation relationswith n degrees of freedom, where 1 n < . 2000 MathematicsSubject Classification 46L57 (primary), 46L53, 46L65 (secondary).     

Numerical Solution of Non-Steady State Porous Flow Free Boundary Problems

The aim of this paper is the study of the convergence of a finite element approximation for a variational inequality related to free boundary problems in non-steady fluid flow through porous media. There have been many results in the stationary case, for example, the steady dam problems, the steady flow well problems, etc. In this paper we shall deal with the axisymmetric non-steady porous flow well problem. It is well know that by means of Torelli's transform this problem, similar to the non-steady rectangular dam problem, can be reduced a variational, inequality, and the existence, uniqueness and regularity of the solution can be obtained ([12, 7]). Now we study the numerical solution of this variational inequality. The main results are as follows: 1. We establish new regularity properties for the solution $W$ of the variation inequality. We prove that $W \in L^\infty(0, T; H^2(D))$, $γ_0W\in L^\infty(0, T; H^2(T_n))$ and $D_1γ_0W\in L^2(0, T; H^1(T_n))$ (see Theorem 2.5). Friedman and Torelli [7] obtained $W\in L^2(0, T; H^2(D))$. Our new regularity properties will be used for error estimation. 2. We prove that the error estimate for the finite element solution of the variational inequality is $$ ( \sum^N_{i=1}\| W^1 - W^1_h \|^2_{H^1(D)}\Delta t)^{1/2} = O(h+\Delta t^{1/2})$$ (see Theorem 3.4). In the stationary case the error estimate is $\|W-W_h\|_{H^1(D)} = O(k)$ ([3,6]). 3. We give a numerical example and compare the result with the corresponding result in the stationary case. The result of this paper are valid for the non-ready rectangular dam problem with stationary or quasi-stationary initial data (see [7], p.534).