共查询到20条相似文献,搜索用时 234 毫秒
1.
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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The upwind finite difference fractional steps method for combinatorial system of dynamics of fluids in porous media and its application 总被引:4,自引:0,他引:4
袁益让 《中国科学A辑(英文版)》2002,45(5):578-593
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. 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
6.
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
7.
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
8.
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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Yirang Yuan 《Numerical Methods for Partial Differential Equations》2008,24(2):400-417
The mathematical model of the three‐dimensional semiconductor devices of heat conduction is described by a system of four quasi‐linear partial differential equations for initial boundary value problem. One equation of elliptic form is for the electric potential; two equations of convection‐dominated diffusion type are for the electron and hole concentration; and one heat conduction equation is for temperature. Upwind finite difference fractional step methods 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 the theory of prior estimates and techniques are adopted. Optimal order estimates in L2 norm are derived to determine the error in the approximate solution.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 相似文献
11.
Lithological discontinuities in a reservoir generate discontinuous coefficients for the first‐order system of equations used in the simulation of fluid flow in porous media. Systems of conservation laws with discontinuous coefficients also arise in many other physical applications. In this article, we present a class of discretization schemes that include variants of mixed finite element methods, finite volume element methods, and cell‐centered finite difference equations as special cases. Error estimates of the order O(h2) in certain discrete L2‐norms are established for both the primary independent variable and its flux, even in the presence of discontinuous coefficients in the flux term. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 267–283, 1999 相似文献
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Zhiyue Zhang 《Numerical Methods for Partial Differential Equations》2009,25(2):259-274
In this article, we study the finite volume element methods for numerical solution of the pollution in groundwater flow in a two‐dimensional convex polygonal domain. These type flow are uniform transport in a fully saturated incompressible porous media, which may be anisotropic with respect to hydraulic conductivity, but features a direction independent of dispersivity. A fully finite volume scheme is analyzed in this article. The discretization is defined via a planar mesh consisting of piecewise triangles. Optimal order error estimates in H1 and L2 norms are obtained. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 相似文献
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Global Existence of Smooth Solutions and Convergence to Barenblatt Solutions for the Physical Vacuum Free Boundary Problem of Compressible Euler Equations with Damping 下载免费PDF全文
For the physical vacuum free boundary problem with the sound speed being C1/2‐Hölder continuous near vacuum boundaries of the one‐dimensional compressible Euler equations with damping, the global existence of the smooth solution is proved, which is shown to converge to the Barenblatt self‐similar solution for the porous media equation with the same total mass when the initial datum is a small perturbation of the Barenblatt solution. The pointwise convergence with a rate of density, the convergence rate of velocity in the supremum norm, and the precise expanding rate of the physical vacuum boundaries are also given. The proof is based on a construction of higher‐order weighted functionals with both space and time weights capturing the behavior of solutions both near vacuum states and in large time, an introduction of a new ansatz, higher‐order nonlinear energy estimates, and elliptic estimates.© 2016 Wiley Periodicals, Inc. 相似文献
14.
Denisa Fericean Teodor Groşan Mirela Kohr Wolfgang L. Wendland 《Mathematical Methods in the Applied Sciences》2013,36(12):1631-1648
In this paper, we describe a layer potential analysis in order to show an existence result for an interface boundary value problem of Robin‐transmission type for the Stokes and Brinkman systems on Lipschitz domains in Euclidean setting, when the given boundary data belong to some Lp or Sobolev spaces associated to such domains. Applications related to an exterior three‐dimensional Stokes flow past two concentric porous spheres with stress jump conditions on the fluid‐porous interface are also considered. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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Bhupen Deka 《Numerical Methods for Partial Differential Equations》2019,35(5):1630-1653
We derive residual‐based a posteriori error estimates of finite element method for linear wave equation with discontinuous coefficients in a two‐dimensional convex polygonal domain. A posteriori error estimates for both the space‐discrete case and for implicit fully discrete scheme are discussed in L∞(L2) norm. The main ingredients used in deriving a posteriori estimates are new Clément type interpolation estimates in conjunction with appropriate adaption of the elliptic reconstruction technique of continuous and discrete solutions. We use only an energy argument to establish a posteriori error estimates with optimal order convergence in the L∞(L2) norm. 相似文献
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We present an H1‐Galerkin mixed finite element method for a nonlinear parabolic equation, which models a compressible fluid flow process in subsurface porous media. The method possesses the advantages of mixed finite element methods while avoiding directly inverting the permeability tensor, which is important especially in a low permeability zone. We conducted theoretical analysis to study the existence and uniqueness of the numerical solutions of the scheme and prove an optimal‐order error estimate for the method. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010 相似文献
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We analyze a combined method consisting of the mixed finite element method for pressure equation and the discontinuous Galerkin method for saturation equation for the coupled system of incompressible two‐phase flow in porous media. The existence and uniqueness of numerical solutions are established under proper conditions by using a constructive approach. Optimal error estimates in L2(H1) for saturation and in L ∞ (H(div)) for velocity are derived. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
19.
Sarvesh Kumar 《Numerical Methods for Partial Differential Equations》2012,28(4):1354-1381
The incompressible miscible displacement problem in porous media is modeled by a coupled system of two nonlinear partial differential equations, the pressure‐velocity equation and the concentration equation. In this article, we present a mixed finite volume element method for the approximation of pressure‐velocity equation and a discontinuous Galerkin finite volume element method for the concentration equation. A priori error estimates in L∞(L2) are derived for velocity, pressure, and concentration. Numerical results are presented to substantiate the validity of the theoretical results. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012 相似文献
20.
Global Well‐Posedness of the Three‐Dimensional Primitive Equations with Only Horizontal Viscosity and Diffusion 下载免费PDF全文
In this paper, we consider the initial boundary value problem of the three‐dimensional primitive equations for planetary oceanic and atmospheric dynamics with only horizontal eddy viscosity in the horizontal momentum equations and only horizontal diffusion in the temperature equation. Global well‐posedness of the strong solution is established for any H2 initial data. An N‐dimensional logarithmic Sobolev embedding inequality, which bounds the L∞‐norm in terms of the Lq‐norms up to a logarithm of the Lp‐norm for p > N of the first‐order derivatives, and a system version of the classic Grönwall inequality are exploited to establish the required a~priori H2 estimates for global regularity.© 2016 Wiley Periodicals, Inc. 相似文献