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....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 ate quite interesting and satisfactory.展开更多
A combined approximate scheme is defined for convection-diffusion-reaction equations. This scheme is constructed by two methods. Standard mixed finite element method is used for diffusion term. A second order characte...A combined approximate scheme is defined for convection-diffusion-reaction equations. This scheme is constructed by two methods. Standard mixed finite element method is used for diffusion term. A second order characteristic finite element method is presented to handle the material derivative term, that is, the time derivative term plus the convection term. The stability is proved and the L2-norm error estimates are derived for both the scalar unknown variable and its flux. The scheme is of second order accuracy in time increment, symmetric, and unconditionally stable.展开更多
针对机载预警雷达空时自适应处理(space-time adaptive processing,STAP)所面临的异构杂波环境,基于杂波和噪声的联合稀疏特性提出了一种直接数据域(direct data domain,D3)STAP方法。首先通过子孔径平滑技术扩充训练样本集合;然后基于...针对机载预警雷达空时自适应处理(space-time adaptive processing,STAP)所面临的异构杂波环境,基于杂波和噪声的联合稀疏特性提出了一种直接数据域(direct data domain,D3)STAP方法。首先通过子孔径平滑技术扩充训练样本集合;然后基于杂波谱二阶表征理论构造STAP功率字典矩阵、导出目标函数,并解得待检测单元信号的空时功率谱;最后根据杂波先验信息重构无孔径损失的杂波加噪声协方差矩阵。数值实验验证了所提方法的协方差矩阵估计精度高于传统的稀疏恢复D3-STAP算法,且在理想情况和存在阵列误差的情况下,所提方法皆具备更好的低速目标检测性能。展开更多
Invertibility is one of the desirable properties of moving average processes. This study derives consequences of the invertibility condition on the parameters of a moving average process of order three. The study also...Invertibility is one of the desirable properties of moving average processes. This study derives consequences of the invertibility condition on the parameters of a moving average process of order three. The study also establishes the intervals for the first three autocorrelation coefficients of the moving average process of order three for the purpose of distinguishing between the process and any other process (linear or nonlinear) with similar autocorrelation structure. For an invertible moving average process of order three, the intervals obtained are , -0.5ρ2ρ1<0.5.展开更多
The physical model is described by a seepage coupled system for simulating numerically three-dimensional chemical oil recovery, whose mathematical description includes three equations to interpret main concepts. The p...The physical model is described by a seepage coupled system for simulating numerically three-dimensional chemical oil recovery, whose mathematical description includes three equations to interpret main concepts. The pressure equation is a nonlinear parabolic equation, the concentration is defined by a convection-diffusion equation and the saturations of different components are stated by nonlinear convection-diffusion equations. The transport pressure appears in the concentration equation and saturation equations in the form of Darcy velocity, and controls their processes. The flow equation is solved by the conservative mixed volume element and the accuracy is improved one order for approximating Darcy velocity. The method of characteristic mixed volume element is applied to solve the concentration, where the diffusion is discretized by a mixed volume element method and the convection is treated by the method of characteristics. The characteristics can confirm strong computational stability at sharp fronts and it can avoid numerical dispersion and nonphysical oscillation. The scheme can adopt a large step while its numerical results have small time-truncation error and high order of accuracy. The mixed volume element method has the law of conservation on every element for the diffusion and it can obtain numerical solutions of the concentration and adjoint vectors. It is most important in numerical simulation to ensure the physical conservative nature. The saturation different components are obtained by the method of characteristic fractional step difference. The computational work is shortened greatly by decomposing a three-dimensional problem into three successive one-dimensional problems and it is completed easily by using the algorithm of speedup. Using the theory and technique of a priori estimates of differential equations, we derive an optimal second order estimates in 12 norm. Numerical examples are given to show the effectiveness and practicability and the method is testified as a powerful tool to solve the important problems.展开更多
In this paper we shall give a simple and easy method to estimate the characteristic exponents for a class of second order linear different equation with periodic coefficient which frequently occurs in application.
基金supported by the Major State Basic Research Development Program of China(G19990328)National Tackling Key Program(2011ZX05011-004+6 种基金2011ZX0505220050200069)National Natural Science Foundation of China(11101244112712311077112410372052)Doctorate Foundation of the Ministry of Education of China(20030422047)
文摘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 ate quite interesting and satisfactory.
文摘A combined approximate scheme is defined for convection-diffusion-reaction equations. This scheme is constructed by two methods. Standard mixed finite element method is used for diffusion term. A second order characteristic finite element method is presented to handle the material derivative term, that is, the time derivative term plus the convection term. The stability is proved and the L2-norm error estimates are derived for both the scalar unknown variable and its flux. The scheme is of second order accuracy in time increment, symmetric, and unconditionally stable.
文摘针对机载预警雷达空时自适应处理(space-time adaptive processing,STAP)所面临的异构杂波环境,基于杂波和噪声的联合稀疏特性提出了一种直接数据域(direct data domain,D3)STAP方法。首先通过子孔径平滑技术扩充训练样本集合;然后基于杂波谱二阶表征理论构造STAP功率字典矩阵、导出目标函数,并解得待检测单元信号的空时功率谱;最后根据杂波先验信息重构无孔径损失的杂波加噪声协方差矩阵。数值实验验证了所提方法的协方差矩阵估计精度高于传统的稀疏恢复D3-STAP算法,且在理想情况和存在阵列误差的情况下,所提方法皆具备更好的低速目标检测性能。
文摘Invertibility is one of the desirable properties of moving average processes. This study derives consequences of the invertibility condition on the parameters of a moving average process of order three. The study also establishes the intervals for the first three autocorrelation coefficients of the moving average process of order three for the purpose of distinguishing between the process and any other process (linear or nonlinear) with similar autocorrelation structure. For an invertible moving average process of order three, the intervals obtained are , -0.5ρ2ρ1<0.5.
基金Supported by the National Natural Science Foundation of China(11101124 and 11271231)Natural Science Foundation of Shandong Province(ZR2016AM08)National Tackling Key Problems Program(2011ZX05052,2011ZX05011-004)
文摘The physical model is described by a seepage coupled system for simulating numerically three-dimensional chemical oil recovery, whose mathematical description includes three equations to interpret main concepts. The pressure equation is a nonlinear parabolic equation, the concentration is defined by a convection-diffusion equation and the saturations of different components are stated by nonlinear convection-diffusion equations. The transport pressure appears in the concentration equation and saturation equations in the form of Darcy velocity, and controls their processes. The flow equation is solved by the conservative mixed volume element and the accuracy is improved one order for approximating Darcy velocity. The method of characteristic mixed volume element is applied to solve the concentration, where the diffusion is discretized by a mixed volume element method and the convection is treated by the method of characteristics. The characteristics can confirm strong computational stability at sharp fronts and it can avoid numerical dispersion and nonphysical oscillation. The scheme can adopt a large step while its numerical results have small time-truncation error and high order of accuracy. The mixed volume element method has the law of conservation on every element for the diffusion and it can obtain numerical solutions of the concentration and adjoint vectors. It is most important in numerical simulation to ensure the physical conservative nature. The saturation different components are obtained by the method of characteristic fractional step difference. The computational work is shortened greatly by decomposing a three-dimensional problem into three successive one-dimensional problems and it is completed easily by using the algorithm of speedup. Using the theory and technique of a priori estimates of differential equations, we derive an optimal second order estimates in 12 norm. Numerical examples are given to show the effectiveness and practicability and the method is testified as a powerful tool to solve the important problems.
基金Supported by Research Foundation of the Fujian Education Bureau (JA04158)the Natural Science Foundation of Fujian Province (No.2006J0209)the Foundation of Developing Science and Technology of Fuzhou University under the grant (2005-XQ-20).
文摘In this paper we shall give a simple and easy method to estimate the characteristic exponents for a class of second order linear different equation with periodic coefficient which frequently occurs in application.
