一类多线性齐性算子的Hardy空间估计 *

证明了一类带齐性核的奇异积分算子的多线性算子是乘积空间L^p1×L^p2 ×…×L^pK(Rⁿ)到Hardy空间H^r(Rⁿ)和弱Hardy空间H^{r ,∞}(Rⁿ)的有界算子 .作为应用 ,获得了一类带齐性核的奇异积分算子交换子的L^p(Rⁿ)有界性 .     

三维动边值问题的特征混合元方法和分析 *

油气运移、聚集史软件的功能是重建盆地发育中油气资源运移、聚集的历史,它对于评估油气资源的勘探和开发有重要的价值.其数学模型是三维空间非线性偶合偏微分方程组的动边值问题.从实际出发,考虑了重力、毛管力和浮力作用的二类边值问题,提出一类特征混合元格式,应用区域变换,处理边界条件的时间变步长技巧,负模估计和先验估计理论,得到最佳阶L²估计。     

三维热传导型半导体问题的差分方法和分析

对2类边值问题提出特征差分格式,利用粗细网块组合、乘积型叁二次插值,处理边界的时间变步长方法、变分形式、先验估计理论和技巧,得到了最佳阶I²误差估计.     

油藏数值模拟中动边值问题的特征差分方法

油气运移、聚集史软件的功能是重建盆地发育中油气资源运移、聚集的历史,它对于合理评估油气资源的勘探和开发有重要的价值。其数学模型是一组非线性偶合偏微分方程组的动边值问题。通过一类特征差分格式,得到了最佳阶的l~2误差估计结果。对这一领域的模型分析、数值方法和软件研制均有重要的理论和实用价值。     

强化采油数值模拟的特征差分方法和I2估计

对于二维、多组分、多相、不可压缩混合流体组成的注化学溶液(如表面活性剂、醇、聚合物)强化采油数值模拟的特征差分方法及其收敛性分析,其数学模型是一组非线性偶合偏微分方程组的初、边值问题。在考虑相互干扰有界区域的一般情况下,本文提出一类特征差分格式,利用粗细网格配套、变分形式、先验估计理论和技巧,得到了最佳阶的l~2误差估计结果。彻底解决了Douglas所提出的著名问题。     

三维动边值问题的迎风差分方法

可压缩可混溶油、水三维渗流动边值问题的研究,对重建盆地发育中油气资源运移、聚集的历史和评估油气资源的勘探与开发有重要的价值, 其数学模型是一组非线性耦合偏微分方程组的动边值问题. 该文对有界域的动边值问题提出一类新的二阶修正迎风差分格式, 应用区域变换、 变分形式、能量方法、差分算子乘积交换性理论、高阶差分算子的分解、微分方程先验估计的理论和技巧, 得到了最佳 $l^2$ 误差估计结果. 该方法已成功应用到油资评估的数值模拟中. 它对这一领域的模型分析, 数值方法和软件研制均有重要的价值.     

三维渗流耦合系统动边值问题迎风差分方法的理论和应用

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.     

两类万有膨胀移位的刻划

本文具体刻划了这样两类万有膨胀移位算子:A_^?0)类单边加权移位和(BCP)_θ类单边加权移位.由此我们回答了一些有关问题.     

可压缩两相驱动问题的分数步长特征差分格式

对可压缩二相渗流驱动问题提出分数步长特征差分格式 ,利用变分形式、能量方法、粗细网格配套、双二次插值、差分算子乘积交替性、高阶差分算子的分解、先验估计的理论和技巧 ,得到最佳阶l² 误差估计 .该方法已成功应用到油资源评估和强化采油数值模拟的生产实际中     

多层渗流方程组合系统的迎风分数步长差分方法和应用

对多层渗流方程组合系统提出适合并行计算的二阶和一阶两类迎风分数步长差分格式,利用变分形式、能量方法、二维和三维格式的配套、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,对二阶格式得到收敛性的最佳阶的L²误差估计. 对一阶格式亦得到收敛性的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评估生产实际中,得到了很好的数值模拟结果.     

THE UPWIND OPERATOR SPLITTING FINITE DIFFERENCE METHOD FOR COMPRESSIBLE TWO-PHASE DISPLACEMENT PROBLEM AND ANALYSIS

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.     

三维多组分可压缩驱动问题的分数步特征差分方法

本文提出三维多组分驱动问题的分数步长特征差分格式,并应用变分形式,能量方法,粗细网格配套,叁二次插值,高阶差分算子的分解和乘积交换性理论和技巧,得到最佳阶L^2误差估计,该方法已成功应用到油资源评估,强化采油数值模拟和海水入侵预测和防治的数值模拟中。     

非线性多层渗流系统的数值方法及其应用

对多层非线性渗流系统提出适合并行计算的迎风分数步差分格式，利用变分形式、能量方法、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误差估计．该方法已成功的应用到油资源渗流力学运移聚集数值模拟的生产实际中．     

The Modified Upwind Finite Difference Fractional Steps Method for Compressible Two-phase Displacement Problem

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.     

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

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.     

The upwind finite difference fractional steps method for combinatorial system of dynamics of fluids in porous media and its application

For combinatorial system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite difference fractional steps 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 implicit-explicit difference scheme, calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. Optimal order estimates in L ² norm are derived to determine the error in the second order approximate solution. This method has already been applied to the numerical simulation of migration-accumulation of oil resources. Keywords: combinatorial system, multilayer dynamics of fluids in porous media, two-class upwind finite difference fractional steps method, convergence, numerical simulation of energy sources.     

渗流耦合系统动边值问题特征分数步差分方法

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一类特征分数步差分格式,利用区域变换、变分形式、粗细网格配套、乘积型叁二次插值、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．     

The upwind finite difference fractional steps methods for two‐phase compressible flow in porous media

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     

The characteristic finite difference fractional steps methods for compressible two-phase displacement problem

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.