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1.
李焕荣 《计算数学》2013,35(1):1-10
本文研究了一维非饱和土壤水流与溶质耦合运移问题的数学模型, 建立了求其数值解的守恒混合元-迎风广义差分格式. 对非线性土壤水分入渗方程, 采用守恒混合元法进行离散模拟, 同时得到了土壤含水量和水分通量; 而对对流-扩散形式的溶质运移方程, 利用迎风的广义差分法离散求解. 且分析了解的存在唯一性, 并讨论了误差估计. 最后给出数值算例, 模拟结果表明利用本文格式来求解非饱和土壤水流与溶质耦合运移问题是可靠的, 且该格式具有稳定性和可实用性.  相似文献   

2.
研究污染物在土壤中运移的时空规律,为土壤环境质量评价及污染预测和防治提供科学的根据与途径,具有重要的理论和实际意义.通过建立土壤中污染物运移问题的全离散守恒混合元格式,讨论了守恒混合元解的存在唯一性,并给出了误差估计.最后给出了数值算例,数值模拟结果表明,用该方法模拟污染物运移问题是合理有效的.  相似文献   

3.
利用无量纲的形式推导出堆浸工艺中通过非饱和堆我动区和滞留区的溶质运移模型,通过最小二乘法确定模型参数,并就两种不同供液情形下的解析解进行了讨论.该模型可用来研究堆浸中溶质浓度的变化规律.  相似文献   

4.
本文对溶质径向运移问题综合了数学模型,考虑了非均衡线性吸附作用和介质的双重性质以及溶质的衰变。在第一类边值条件下,用Laplace变换求得了严格的解析解。用FORTRAN程序在DJS-040机上对无量纲化的问题解进行了计算。求出了浓度的分布和变化,讨论了有实际意义的各种极限情况并给出了相应的解,通过数值分析,得出了几点有价值的结论。  相似文献   

5.
蒸汽沉淀化学反应过程有着极其广泛的应用,其数学模型归结为一个包含流速场,温度场,压力场和气体溶质场的非线性偏微分方程组.用混合有限元方法研究蒸汽沉淀化学反应方程组,导出其半离散化和全离散化的混合元格式,并证明这些格式的解的存在性和收敛性(误差估计).用混合元法处理究蒸汽沉淀化学反应方程组,可以同时求出流速场,温度场,压力场和气体溶质场的数值解.因此该研究既具有重要的理论意义,又具有广泛的应用前景.  相似文献   

6.
油水运移聚集数值模拟和分析   总被引:6,自引:1,他引:5  
油资源的运移聚集数值模拟是描述在盆地发育中油水运移聚集演化的历史,它对于油田的勘探和合理开发有着重要的价值·本文提出问题的数学模型和修正交替方向隐式迭式格式·对于著名的二次运移聚集的水动力学实验(剖面和平面问题),进行了数值模拟,模拟结果和实验结果是完全吻合的·  相似文献   

7.
针对储气库开采过程中油侵气窜的问题,以喇嘛甸北部为研究对象,对储气库油气界面的运移进行监测,分别通过物理模拟方法和数值模拟方法研究油侵气窜与油气区压差的关系,进而得到生产过程中油区气区之间的合理压差.物理模拟研究表明,当油气区压差超过一定值时,油气界面会发生运移,压差越大,油气界面运移距离越远;数值模拟研究表明,储气库油侵气窜压差界限为±0.5MPa;通过矿场监测论证,最终确认上述压差界限的合理性.  相似文献   

8.
滩海地区运移聚集的精细数值模拟和分析   总被引:1,自引:1,他引:0  
对滩海地区三层油资源运移聚集进行高精度精细平行数值模拟,提出数学模型和精细平行算子分裂隐式迭代格式,设计了并行计算程序,提出了并行计算的信息传递和交替方向网格剖分方法.并对不同的CPU组合进行并行计算和分析,对滩海地区数值模拟结果和实际情况吻合.对模型问题进行数值分析,得到最佳阶误差估计,成功地解决了这一困难问题·  相似文献   

9.
基于混合编码的混合遗传算法   总被引:2,自引:0,他引:2  
本文研究了神经网络优化问题.利用混合编码的方法,结合遗传算法与共轭梯度法的优点,得到一种基于混合编码的混合遗传算法.数值模拟结果表明,混合算法既具有较快的收敛速度,又能够收敛到全局最优解.  相似文献   

10.
三维油资源运移聚集的模拟和应用   总被引:4,自引:2,他引:2  
盆地发育的运移聚集史数值模拟, 其功能是重建油气盆地的运移聚集演化史, 它对于油资源的勘探, 确定油藏位置和计算油藏贮量, 寻找新的油田, 具有极其重要的价值·  本文从地质科学实际出发, 研究了三维问题的地质和渗流力学特征, 提出二阶修正算子分裂隐式迭代格式, 对著名油水运移聚集实验进行了数值模拟, 结果基本吻合, 并对胜利油田东营凹陷的实际问题进行数值模拟试验, 结果和实际地质情况( 油田位置等) 基本吻合, 成功解决了这一著名问题·  相似文献   

11.
非饱和水流问题的混合元法及其数值模拟   总被引:4,自引:0,他引:4  
1.引 言 均质土壤中的地下水流动可归结为非饱和土壤水的流动,是土壤水未完全充满孔隙时的流动,是多孔介质流体运动的一种重要形式.非饱和流动的预报在大气科学、土壤学、农业  相似文献   

12.
In this paper, we investigate the superconvergence of fully discrete splitting positive definite mixed finite element (MFE) methods for parabolic optimal control problems. For the space discretization, the state and co-state are approximated by the lowest order Raviart–Thomas MFE spaces and the control variable is approximated by piecewise constant functions. The time discretization of the state and co-state are based on finite difference methods. We derive the superconvergence between the projections of exact solutions and numerical solutions or the exact solutions and postprocessing numerical solutions for the control, state and co-state. A numerical example is provided to validate the theoretical results.  相似文献   

13.
In this article, a reduced mixed finite element (MFE) formulation based on proper orthogonal decomposition (POD) for the non-stationary conduction-convection problems is presented. Also the error estimates between the reduced MFE solutions based on POD and usual MFE solutions are derived. It is shown by numerical examples that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced MFE formulation based on POD is feasible and efficient in finding numerical solutions for the non-stationary conduction-convection problems.  相似文献   

14.
15.
This paper considers how the Moving Finite Element (MFE) methodapproxim ates the steady and large time solutions of a familyof linear diffusion equations in one space dimension. In particular,it is shown that any steady solution to the Moving Finite Elementequations must satisfy the stationary equations for a best approximationto the steady solution of the PDE from the manifold of free-knotlinear splines, in some problem dependent norm. For the special case of the inhomogeneous linear heat equationit is also shown that, under certain conditions, the only steadyMFE solution is the unique global best fit to the true steadysolution, in the H1 semi-norm. It is also demonstrated numericallythat these steady solutions are stable attractors. Finally,a numerical study of the large time solutions of the homogeneouslinear heat equation is undertaken and it is demonstrated thatthe MFE solutions appear to possess a rather novel temporalaccuracy property.  相似文献   

16.
This article deals with development and analysis of a numerical method for a coupled system describing miscible displacement of one incompressible fluid by another through heterogeneous porous media. A mixed finite element (MFE) method is employed to discretize the Darcy flow equation combined with a conservative finite volume (FV) method on unstructured grids for the concentration equation. It is shown that the FV scheme satisfies a discrete maximum principle. We derive L and BV estimates under an appropriate CFL condition. Then we prove convergence of the approximate solutions to a weak solution of the coupled system. Numerical results are presented to see the performance of the method in two space dimensions. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008  相似文献   

17.
In this study, we employ mixed finite element(MFE) method, two local Gauss integrals, and parameter-free to establish a stabilized MFE formulation for the non-stationary incompressible Boussinesq equations. We also provide the theoretical analysis of the existence,uniqueness, stability, and convergence of the stabilized MFE solutions for the stabilized MFE formulation.  相似文献   

18.
In this article, a coupling method of new mixed finite element (MFE) and finite element (FE) is proposed and analyzed for fourth-order parabolic partial differential equation. First, the fourth-order parabolic equation is split into the coupled system of second-order equations. Then, an equation is solved by finite element method, the other equation is approximated by the new mixed finite element method, whose flux belongs to the square integrable space replacing the classical H(div;Ω) space. The stability for fully discrete scheme is derived, and both semi-discrete and fully discrete error estimates are obtained. Moreover, the optimal a priori error estimates in L 2 and H 1-norm for both the scalar unknown u and the diffusion term γ and a priori error estimate in (L 2)2-norm for its flux σ are derived. Finally, some numerical results are provided to validate our theoretical analysis.  相似文献   

19.
Summary We discuss semi-discrete three-point finite difference methods for the numerical solution of system of conservation laws which are second order accurate in space in the sense of truncation error. Particular discretizations of the numerical entropy flux associated with such schemes are studied clarifying the importance of this discretization with regard to the production of numerical entropy. Using a numerical entropy flux constructed in a canonical way we prove that a wide class of finite difference methods cannot satisfy a discrete entropy inequality. Together with a well known result of Schonbek concerning Lax-Wendroff type schemes our result indicates a strong relationship between entropy production and oscillations in numerical solutions.The research reported here was supported by a grant from the Stiftung Volkswagenwerk, Federal Republic of Germany. It is a part of the doctoral thesis of the above author, Universität Stuttgart, 1991.  相似文献   

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