油水渗流动边值问题的迎风差分方法

可压缩可混溶油、水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.对二维有界域的动边值问题提出一类新的迎风差分格式,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.     

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。     

二维可压缩油水两相渗流动边值问题的特征差分方法

可压缩可混溶油、水两相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偶合偏微分方程组的动边值问题．本文对二维有界域的两类边值问题提出一类新的特征差分格式,应用区域变换、时间的变步长、粗细网格配套、变分形式、先验估计的理论和技巧,得到了最佳阶l2误差估计结果．将J．Douglas,Jr．提出的著名方法,成功地拓广到这一新领域,并得到实质性进展．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．     

非线性渗流耦合系统动边值问题二阶迎风分数步差分方法

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.     

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.     

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．     

渗流耦合系统动边值问题特征差分方法及其应用

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．其数学模型是一组多层对流扩散耦合系统的动边值问题．提出一类特征差分格式,得到最佳阶误差估计结果．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．     

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。     

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     

三维非线性对流扩散问题的数值方法在渗流力学的应用

对三维非线性对流扩散问题提出一类适合并行计算的二阶迎风分数步差分格式,采用分数步技术,将三维问题化为连续解3个一维问题计算．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、微分方程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油资源运移聚集渗流力学数值模拟计算、海水入侵预测和防治的工程实践中．     

THE UPWIND FINITE DIFFERENCE METHOD FOR MOVING BOUNDARY VALUE PROBLEM OF COUPLED SYSTEM

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.     

The second‐order upwind finite difference fractional steps method for moving boundary value problem of oil‐water percolation

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     

Stationary micropolar fluid with boundary data in L

We consider the Dirichlet boundary value problem for the equations of a stationary micropolar fluid in a bounded three-dimensional domain. We show the existence and uniqueness of a distributional solution with boundary values in L².     

On the convergence of the heat balance integral method

Convergence properties are established for the piecewise linear heat balance integral solution of a benchmark moving boundary problem, thus generalising earlier results [Numer. Heat Transfer 8 (1985) 373]. A convergence rate of O(n⁻¹) is identified with minor effects at large values of the Stefan number β (slow interface movement). The correct O(n^−1/2) behaviour for incident heat flux is recovered for β → 0 (pure heat conduction) as previously found [Numer. Heat Transfer 8 (1985) 373–382]. Numerical illustrations support the theoretical findings.     

Computational modelling of fluid structure interaction at nano-scale boundaries with modified Maxwellian velocity distribution

The soft collisions among fluid–fluid and fluid-wall molecules are modeled from first principles. In particular, the assumption of Maxwellian distribution of velocities for thermalized molecules, in both parallel and perpendicular directions to the wall, has been re-evaluated with supporting experimental and/or numerical evidence.It is proposed that the normal component of molecular velocity post collision is conserved for all fluid molecules. The slip effect at the wall boundary, introduced by the surface roughness, is accounted by an accommodation coefficient f. A moving least square method is used to calculate macroscopic velocity values. The influence of molecular interaction on the macroscopic velocity distribution is investigated at 40 MPa and 300 K for slit pore, inclined and stepped wall configurations. The accommodation coefficient values f = 0, 0.07, 0.257, 0.45, 0.681 and 1; and acceleration values ranging from zero to 1 × 10¹¹ m/s² and 250 × 10¹¹ m/s² are used for comparison.The distribution of macroscopic velocity parallel to the wall is studied to observe the effect of the slip behaviour. The detailed study of average of velocity values at various magnitudes of acceleration has shown an evidence of characteristic low and high speed of molecular flows that is considered as significant and a comparison is sought with an equivalent laminar and turbulent flow style behaviour. The two dimensional vector and contour plots of macroscopic velocity provide further insights in understanding Continuum velocity distributions resulting from molecular fluid-wall interaction at nanoscale. The research has highlighted the need to develop molecular dynamics simulation techniques for non-periodic boundary conditions.     

Gas dynamics applications of a characteristic Cauchy problem

Some initial-boundary-value problems for a system of quasilinear partial differential equations of gas dynamics with the initial data prescribed on the characteristic surface (characteristic Cauchy problem) are considered. The following three-dimensional flow problems are investigated: the flow produced by a motion of an impermeable piston; the flow produced by a permeable piston with a given pressure; and the flow produced by the moving free boundary. In the first two problems, the piston motion is prescribed; in the last problem, the free boundary motion cannot be prescribed in advance and must be determined as a part of the problem. It is shown that those problems can be reduced to a characteristic Cauchy problem of a certain standard type that satisfies the analog of Cauchy-Kowalewski's existence theorem in the class of analytical functions (Differential Equations 12 (1977) 1438-1444). Thus, it is proved that, in the case of the analyticity of the input data, the considered problems have unique piecewise analytic solutions which may be expressed by infinite power series (the procedure of constructing the power series solution is described in Differential Equations 12 (1977) 1438-1444 as a part of the proof of the theorem).     

Effect of variable density on hydromagnetic mixed convection flow of a non-Newtonian fluid past a moving vertical plate

The effect of temperature-dependent density on MHD mixed convection flow of power-law fluid past a moving semi-infinite vertical plate for high temperature differences between the plate and the ambient fluid is studied. The fluid density is assumed to decrease exponentially with temperature. The usual Boussinesq approximations are not considered due to the large temperature differences. The surface temperature of the moving plate was assumed to vary according to a power-law form, that is, T_w(x) = T_∞ + Ax^γ. The fluid is permeated by a uniform magnetic field imposed perpendicularly to the plate on the assumption of small magnetic Reynolds number. A numerical shooting algorithm for two unknown initial conditions with fourth-order Runge–Kutta integration scheme has been used to solve the coupled non-linear boundary value problem. The effects of various parameters on the velocity and temperature profiles as well as the local skin-friction coefficient and the local Nusselt number are presented graphically and in the tabular form. The results show that application of Boussinesq approximations in a non-Newtonian fluid subjected to high temperature differences gives a significant error in the values of the skin-friction coefficient and the application of an external magnetic field reduces this error markedly in the case of shear-thickening fluid.     

The problem of the nonlinear diffusive predator–prey model with the same biotic resource

In recent years, the research on the diffusive predator–prey model has attracted much attention. In these models, the carrying capacity is considered as a constant. In 2013, H. M. Safuan investigated the system of a predator and prey that shares the same biotic resource, where the carrying capacity is a function of the time. The spatial component of ecological interactions has been recognized as an important factor. So, we will discuss the problem of the nonlinear diffusive predator–prey model with the same biotic resource. This model is the system of the nonlinear partial differential equations with zero-flux boundary condition. The main objective of the present paper is to investigate the existence and uniqueness of the solution of this model. In this paper, we also obtain that there is a unique solution of the nonlinear partial differential equations with Dirichlet boundary condition.