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THE UPWIND FINITE DIFFERENCE FRACTIONAL STEPS METHOD FOR NONLINEAR COUPLED SYSTEM OF DYNAMICS OF FLUIDS IN POROUS MEDIA

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Journal of Systems Science & Complexity 2006年第4期19卷 498-516页

作者： yirang yuan Institute of Mathematics Shandong University Jinan 250100 China.

为在多孔的媒介的液体的多层的动力学的非线性的联合系统，第二订；首先订迎风的有限差别对平行算术适用的部分步计划被提出，；二维；三维的计划被用来形成一个完全的集合。一些技术例如变化的演算，差别操作员的趋于增加的交换统治，... 详细信息

为在多孔的媒介的液体的多层的动力学的非线性的联合系统，第二订；首先订迎风的有限差别对平行算术适用的部分步计划被提出，；二维；三维的计划被用来形成一个完全的集合。一些技术例如变化的演算，差别操作员的趋于增加的交换统治，高顺序差别操作员的分解；优先的估计，被采用。在 L 的最佳的顺序估计[2 ] 标准被导出在第二份订单决定错误近似答案。这个方法已经被用于油资源的迁居累积的数字模拟。

关键词：分数步幅非线性连接系统流体动力学多孔渗水介质

An Upwind Mixed Volume Element-Fractional Step Method on a Changing Mesh for Compressible Contamination Treatment from Nuclear Waste

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Advances in Applied Mathematics and Mechanics 2018年第6期10卷 1384-1417页

作者： Changfeng Li yirang yuan Huailing Song Institute of Mathematics Shandong UniversityJinan 250100China School of Economics Shandong UniversityJinan 250100China College of Mathematics and Econometrics Hunan UniversityChangsha 410082China

In this paper the authors discuss the numerical simulation problem of threedimensional compressible contamination treatment from nuclear waste.The mathematical model is defined by an initial-boundary nonlinear convection-diffusion system of four partial differential equations:a parabolic equation for the pressure,two convection-diffusion equations for the concentrations of brine and radionuclide and a heat conduction equation for the temperature.The pressure appears within the concentration equations and heat conduction equation,and the Darcy velocity controls the concentrations and the temperature.The pressure is solved by the conservative mixed volume element method,and the order of the accuracy is improved by the Darcy velocity.The concentration of brine and temperature are computed by the upwind mixed volume element method on a changing mesh,where the diffusion is discretized by a mixed volume element and the convection is treated by an upwind scheme.The composite method can solve the convection-dominated diffusion problems well because it eliminates numerical dispersion and nonphysical oscillation and has high order computational accuracy.The mixed volume element has the local conservation of mass and energy,and it can obtain the brine and temperature and their adjoint vector functions simultaneously.The conservation nature plays an important role in numerical simulation of underground fluid.The concentrations of radionuclide factors are solved by the method of upwind fractional step difference and the computational work is decreased by decomposing a three-dimensional problem into three successive one-dimensional problems and using the method of speedup.By the theory and technique of a priori estimates of differential equations,we derive an optimal order result in L^(2) norm.Numerical examples are given to show the effectiveness and practicability and the composite method is testified as a powerful tool to solve the well-known actual problem.

关键词： Compressible nuclear waste contamination in porous media upwind mixed volume element-fractional step on a changing mesh conservation of mass and energy convergence analysis numerical example

Theory and application of numerical simulation method of capillary force enhanced oil production

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Applied Mathematics and Mechanics(English Edition) 2015年第3期36卷 379-400页

作者： yirang yuan Aijie CHENG Danping YANG Changfeng LI Yunxin LIU Institute of Mathematics Shandong University

A kind of second-order implicit upwind fractional step finite difference methods are presented for the numerical simulation of coupled systems for enhanced （chemical） oil production with capillary force in the porous media. Some techniques, e.g., the calculus of variations, the energy analysis method, the commutativity of the products of difference operators, the decomposition of high-order difference operators, and the theory of a priori estimate, are introduced. An optimal order error estimate in the l2 norm is derived. The method is successfully used in the numerical simulation of the enhanced oil production in actual oilfields. The simulation results are satisfactory and interesting.

关键词： enhanced （chemical） oil production system on consideration ference optimal order l2 capillary force second-order three-dimensional porous coupled implicit upwind fractional step difestimate application in actual oilfield

An Upwind Finite Volume Element Method for Nonlinear Convection Diffusion Problem

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American Journal of Computational Mathematics 2011年第4期1卷 264-270页

作者： Fuzheng Gao yirang yuan Ning Du 不详

A class of upwind finite volume element method based on tetrahedron partition is put forward for a nonlinear convection diffusion problem. Some techniques, such as calculus of variations, commutating operators and the a priori estimate, are adopted. The a priori error estimate in L2-norm and H1-norm is derived to determine the error between the approximate solution and the true solution.

关键词： Nonlinear Convection-Diffusion Tetrahedron Partition Error Estimates

The Theory and Application of Upwind Finite Difference Fractional Steps Procedure for Seawater Intrusion

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International Journal of Geosciences 2012年第5期3卷 972-991页

作者： yirang yuan Hongxing Rui Dong Liang Changfeng Li Institute of Mathematics Shandong University Jinan China

Numerical simulation and theoretical analysis of seawater intrusion is the mathematical basis for modern environmental science. Its mathematical model is the nonlinear coupled system of partial differential equations with initial-boundary problems. For a generic case of a three-dimensional bounded region, two kinds of finite difference fractional steps pro- cedures are put forward. Optimal order estimates in norm are derived for the error in the approximation solution. The present method has been successfully used in predicting the consequences of seawater intrusion and protection projects.

关键词： Seawater Intrusion Three-Dimensional Region Upwind Fractional Steps Norm Estimate Numerical Simulation

Theory and Application of Numerical Simulation of Chemical Flooding in High Temperature and High Salt Reservoirs

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International Journal of Geosciences 2014年第9期5卷 956-970页

作者： yirang yuan Aijie Cheng Danping Yang Changfeng Li Institute of Mathematics Shandong University Jinan China

Applications, theoretical analysis and numerical methods are introduced for the simulation of mechanical models and principles of the porous flow in high temperature, high salt, complicated geology and large-scale reservoirs in this paper. Considering petroleum geology, geochemistry, computational permeation fluid mechanics and computer technology, we state the models of permeation fluid mechanics and put forward a sequence of implicit upwind difference iteration schemes based on refined fractional steps of the upstream, which can compute the pressures, the saturation and the concentrations of different chemistry components. A type of software applicable in major industries has been completed and carried out in numerical analysis and simulations of oil extraction in Shengli Oil-field, which brings huge economic benefits and social benefits. This software gives many characters: spatial steps are taken as ten meters, the number of nodes is up to hundreds of thousands and simulation time period can be tens of years and the high-order accuracy can be promised in numerical data. Precise analysis is present for simplified models of this type and that provides a tool to solve the international famous problem.

关键词： High Temperature and High Salt Complicated Chemical Flooding Computational Permeation Fluid Mechanics Numerical Method and Engineering Software Actual Application of Oil-Fields Theoretical Analysis

The finite difference method for the three-dimensional nonlinear coupled system of dynamics of fluids in porous media

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Science China Mathematics 2006年第2期49卷 185-211页

作者： yuan yirang Institute of Mathematics Shandong University Jinan 250100 China

For the three-dimensional coupled system of multilayer dynamics of fluids in porous media, the second-order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Some techniques, such as calculus of variations, energy method,multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in l2 norm are derived to determine the error in the second-order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources.

关键词： multilayer coupled system nonlinear equations upwind finite difference fractional steps convergence numerical simulation.

A MIXED FINITE ELEMENT AND CHARACTERISTIC MIXED FINITE ELEMENT FOR INCOMPRESSIBLE MISCIBLE DARCY-FORCHHEIMER DISPLACEMENT AND NUMERICAL ANALYSIS

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数学物理学报:B辑英文版 2023年第5期43卷 2026-2042页

作者：袁益让李长峰孙同军杨青 Institute of Mathematics Shandong UniversityJinan 250100China School of Economics Shandong UniversityJinan 250100China School of Mathematical Sciences Shandong Normal UniversityJinan 250014China

In this paper a mixed finite element-characteristic mixed finite element method is discussed to simulate an incompressible miscible Darcy-Forchheimer problem.The flow equation is solved by a mixed finite element and the approximation accuracy of Darch-Forchheimer velocity is improved one order.The concentration equation is solved by the method of mixed finite element,where the convection is discretized along the characteristic direction and the diffusion is discretized by the zero-order mixed finite element method.The characteristics can confirm strong stability at sharp fronts and avoids numerical dispersion and nonphysical oscillation.In actual computations the characteristics adopts a large time step without any loss of accuracy.The scalar unknowns and its adjoint vector function are obtained simultaneously and the law of mass conservation holds in every element by the zero-order mixed finite element discretization of diffusion flux.In order to derive the optimal 3/2-order error estimate in L^(2) norm,a post-processing technique is included in the approximation to the scalar unknowns.Numerical experiments are illustrated finally to validate theoretical analysis and efficiency.This method can be used to solve such an important problem.

关键词： Darcy-Forchheimer miscible displacement mixed element-characteristic mixed element-postprocessing scheme local conservation of mass 3/2-order error estimates in L^(2)-norm numerical computation

The numerical simulation and analysis of three-dimensional seawater intrusion and protection projects in porous media

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Science China(Physics,Mechanics & Astronomy) 2009年第1期52卷 92-107页

作者： yuan yirang LIANG Dong RUI HongXing Institute of Mathematics Shandong UniversityJinan 250100China

For the three-dimensional seawater intrusion and protection system, the model of dynamics of fluids in porous media and the modified upwind finite difference fractional steps schemes are put forward. Based on the numerical simulation of the practical situation in the Laizhou Bay Area of Shandong Province, predictive numerical simulation and analysis of the consequence of protection projects, underground dams, tidal barrage projects and the applied modular form of project adjustment have been finished. By using the theory and techniques of differential equation prior estimates, the convergence results have been got.

关键词： seawater intrusion and protection the model of dynamics of fluids in porous media upwind fraction steps