共查询到20条相似文献,搜索用时 31 毫秒
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Yirang Yuan 《Numerical Methods for Partial Differential Equations》2007,23(5):1037-1058
For nonlinear coupled system of multilayer dynamics of fluids in porous media, a second‐order upwind finite‐difference fractional‐steps scheme applicable to parallel arithmetic are put forward, and two‐ and three‐dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, 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 approximate solution. This method has already been applied to the numerical simulation of migration‐accumulation of oil resources. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 相似文献
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对多层非线性渗流方程耦合系统三维动边值问题, 提出适合并行计算的一类二阶迎风分数步差分格式, 利用区域变换、变分形式、能量方法、隐显格式的相互结合、差分算子乘积交换性、高阶差分算子的分解、先验估计的理论和技巧, 得到收敛性的最佳阶l2 误差估计. 该方法已成功地应用到多层油资源运移聚集的资源评估生产实际中, 得到了很好的数值模拟结果. 相似文献
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The finite difference method for the three-dimensional nonlinear coupled system of dynamics of fluids in porous media 总被引:2,自引:0,他引:2
YUAN Yirang Institute of Mathematics Shandong University Jinan China 《中国科学A辑(英文版)》2006,49(2):185-211
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. 相似文献
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Yirang Yuan 《Numerical Methods for Partial Differential Equations》2003,19(5):665-681
For the coupled system of multilayer fluid dynamics in porous media, the modified characteristic finite difference fractional steps method applicable to parallel arithmetic is put forward and two‐dimensional and three‐dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, energy method, piecewise biquadratic interpolation, 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 approximate solution. This method has already been applied to the numerical simulation of multilayer fluid dynamics in porous media. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 665–681, 2003. 相似文献
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袁益让 《数学物理学报(A辑)》2009,29(4):858-872
对多层非线性渗流耦合系统提出适合并行计算的特征分数步差分格式, 利用变分形式、能量方法、粗细网格配套、分片双二次插值、差分算子乘积交换性、高阶差分算子的分解、先验估计的理论和技巧, 得到收敛性的最佳阶的l2误差估计. 该方法已成功的应用到多层油资源评估的生产实际中. 相似文献
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对多层渗流方程耦合系统动边值问题,提出适合并行计算的两类迎风差分格式,利用区域变换、变分形式、能量方法、隐显格式的相互结合、差分算子乘积交换性、高阶差分算子的分解、先验估计的理论和技巧,得到收敛性的l~2误差估计.该方法已成功地应用到多层油资源运移聚集的资源评估生产实际中,得到了很好的数值模拟结果. 相似文献
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Yirang Yuan 《Numerical Methods for Partial Differential Equations》2003,19(1):67-88
The upwind finite difference fractional steps methods are put forward for the two‐phase compressible displacement problem. Some techniques, such as calculus of variations, 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 approximate solution. This method has already been applied to the numerical simulation of seawater intrusion and migration‐accumulation of oil resources. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 67–88, 2003 相似文献
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袁益让 《数学物理学报(B辑英文版)》2011,31(3):857-881
Coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of prospecting and exploiting oil-gas resources.The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values.The upwind finite difference schemes applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set.Some techniques,such as change of variables,calculus of variations, multiplicative commutation rule of difference operators,decomposition of high order difference operators and prior estimates,are adopted.The estimates in l~2 norm are derived to determine the error in the approximate solution.This method was already applied to the numerical simulation of migration-accumulation of oil resources. 相似文献
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《数学物理学报(B辑英文版)》2015,(6)
A kind of second-order implicit fractional step characteristic finite difference method is presented in this paper for the numerically simulation coupled system of enhanced(chemical) oil production in porous media.Some techniques,such as the calculus of variations,energy analysis method,commutativity of the products of difference operators,decomposition of high-order difference operators and the theory of a priori estimates are introduced and an optimal order error estimates in l~2 norm is derived.This method has been applied successfully to the numerical simulation of enhanced oil production in actual oilfields,and the simulation results are quite interesting and satisfactory. 相似文献
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Yi-rangYuan 《应用数学学报(英文版)》2004,20(3):381-396
For compressible two-phase displacement problem,the modified upwind finite difference fractionalsteps schemes are put forward.Some techniques,such as calculus of variations,commutative law of multiplicationof difference operators,decomposition of high order difference operators,the theory of prior estimates and tech-niques are used.Optimal order estimates in L~2 norm are derived for the error in the approximate solution.Thismethod has already been applied to the numerical simulation of seawater intrusion and migration-accumulationof oil resources. 相似文献
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Yuan Yirang Li Changfeng Sun Tongjun 《Numerical Methods for Partial Differential Equations》2014,30(4):1103-1129
The research of the three‐dimensional (3D) compressible miscible (oil and water) displacement problem with moving boundary values is of great value to the history of oil‐gas transport and accumulation in basin evolution, as well as to the rational evaluation in prospecting and exploiting oil‐gas resources, and numerical simulation of seawater intrusion. The mathematical model can be described as a 3D‐coupled system of nonlinear partial differential equations with moving boundary values. For a generic case of 3D‐bounded region, a kind of second‐order upwind finite difference fractional steps schemes applicable to parallel arithmetic is put forward. Some techniques, such as the change of variables, calculus of variations, and the theory of a priori estimates, are adopted. Optimal order estimates in l2 norm are derived for the errors in approximate solutions. The research is important both theoretically and practically for model analysis in the field, for model numerical method and for software development. Thus, the well‐known problem has been solved.Copyright © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1103–1129, 2014 相似文献
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The characteristic finite difference fractional steps methods for compressible two-phase displacement problem 总被引:3,自引:0,他引:3
Yirang Yuan 《中国科学A辑(英文版)》1999,42(1):48-57
For compressible two-phase displacement problem, a kind of characteristic finite difference fractional steps schemes is put
forward and thick and thin grids are used to form a complete set. Some techniques, such as piecewise biquadratic interpolation,
of calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference
operators and prior estimates are adopted. Optimal order estimates inL
2 norm are derived to determine the error in the approximate solution.
Project supported by the National Scaling Program, the National Tackling Key Problems Program and the Doctorate Foundation
of the State Education Commission of China. 相似文献
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In the past decades, the finite difference methods for space fractional operators develop rapidly; to the best of our knowledge, all the existing finite difference schemes, including the first and high order ones, just work on uniform meshes. The nonlocal property of space fractional operator makes it difficult to design the finite difference scheme on non-uniform meshes. This paper provides a basic strategy to derive the first and high order discretization schemes on non-uniform meshes for fractional operators. And the obtained first and second schemes on non-uniform meshes are used to solve space fractional diffusion equations. The error estimates and stability analysis are detailedly performed; and extensive numerical experiments confirm the theoretical analysis or verify the convergence orders. 相似文献
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袁益让 《数学物理学报(B辑英文版)》2002,22(4)
For compressible two-phase displacement problem, a kind of upwind operator splitting finite difference schemes is put forward and make use of operator splitting, of calculus of variations, multiplicative commutation rule of difference operators, decompo-sition of high order difference operators and prior estimates are adopted. Optimal order estimates in L2 norm are derived to determine the error in the approximate solution. 相似文献