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

doi:10.1016/S0252-9602(11)60282-8

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (3): 857-881.doi: 10.1016/S0252-9602(11)60282-8

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

袁益让

Institute of Mathematics, Shandong University, Jinan 250100, China

收稿日期:2009-07-13 修回日期:2009-11-16 出版日期:2011-05-20 发布日期:2011-05-20
基金资助:
This work is supported by the Major State Basic Research Program of China (19990328), the National Tackling Key Problem Programs (20050200069), the National Natural Science Foundation of China (10771124; 10372052), the Doctorate Foundation of the Ministry of Education of China (20030422047), Shandong Provance Natural Science Foundation (2R2009AQ12), and the Independent Innovation Foundation of Shandong University (2010TS031).

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

YUAN Yi-Rang

Institute of Mathematics, Shandong University, Jinan 250100, China

Received:2009-07-13 Revised:2009-11-16 Online:2011-05-20 Published:2011-05-20
Supported by:
This work is supported by the Major State Basic Research Program of China (19990328), the National Tackling Key Problem Programs (20050200069), the National Natural Science Foundation of China (10771124; 10372052), the Doctorate Foundation of the Ministry of Education of China (20030422047), Shandong Provance Natural Science Foundation (2R2009AQ12), and the Independent Innovation Foundation of Shandong University (2010TS031).

摘要/Abstract

摘要：

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 ²norm 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.

关键词: multilayer coupled system, moving boundary values, upwind finite difference method, convergence, numerical simulation of energy

Abstract:

Key words: multilayer coupled system, moving boundary values, upwind finite difference method, convergence, numerical simulation of energy sources

中图分类号:

65M06

袁益让. THE UPWIND FINITE DIFFERENCE METHOD FOR MOVING BOUNDARY VALUE PROBLEM OF COUPLED SYSTEM[J]. 数学物理学报(英文版), 2011, 31(3): 857-881.

YUAN Yi-Rang. THE UPWIND FINITE DIFFERENCE METHOD FOR MOVING BOUNDARY VALUE PROBLEM OF COUPLED SYSTEM[J]. Acta mathematica scientia,Series B, 2011, 31(3): 857-881.

参考文献

[1] Ewing R E. The Mathematics of Reservoir Simulation. Philadelphia: SIAM, 1983

[2] Bredehoeft J D, Pinder G F. Digital analysis of areal flow in multiaquifer groundwater systems: A quasi-three-dimensional model. Water Resources Research, 1970, 6(3): 883--888

[3] Don W, Emil O F. An iterative quasi-three-dimensional finite element model for heterogeneous multiaquifer systems. Water Resources Research, 1978, 14(5): 943--952

[4] Ungerer P, et al. Migration of Hydrocarbon in Sedimentary Basins. Paris: Editions Techniq, 1987: 414--455

[5] Ungerer P. Fluid flow, hydrocarbon generation and migration. AAPG Bull, 1990, 74(3): 309--335

[6] Douglas Jr J, Russell T F. Numerical method for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures. SIAM J Numer Anal, 1982, 19(5): 871--885

[7] Douglas Jr J. Finite difference methods for two-phase incompressible flow in porous media. SIAM J Numer Anal, 1983, 20(4): 681--696

[8] Bermudez A, Nogueiras M R, Vazquez C. Numerical analysis of convection-diffusion-reaction problems with higher order
characteristics/finite elements. Part I: time diseretization. SIAM J Numer Anal, 2006, 44(5): 1829--1853

[9] Bermudez A, Nogueriras M R, Vazquez C. Numerical analysis of convection-diffusion-reaction problems with higher order
characteristics/finite elements. Part II: fully diseretized scheme and quadratare fomulas. SIAM J Numer Anal, 2006, 44(5):1854--1876.

[10] Peaceman D W. Fundamental of Numerical Reservoir Simulation. Amsterdam: Elsevier, 1980

[11] Ewing R E, Lazarov R D, Vassilev A T. Finite difference scheme for parabolic problems on a composite grids with refinement in time and space. SIAM J Numer Anal, 1994, 31(6): 1605--1622

[12] Lazarov R D, Mischev I D, Vassilevski P S. Finite volume methods for convection-diffusion problems. SIAM J Numer Anal, 1996, 33(1): 31--55

[13] Marchuk G I. Splitting and alternating direction method//Ciarlet P G, Lions J L, eds. Handbook of Numerical Analysis. Paris: Elesevior Science Publishers, B V, 1990: 197--460

[14] Yuan Y R. The upwind finite difference fractional steps method for combinatorial system of dynamics of fluids in porous media and its application. Science in China, Series A, 2002, 45(5): 578--593.

[15] Yuan Y R. The finite difference method for the three-dimensional nonlinear coupled system of dynamics of fluids in porous media. Science in China, Series A, 2006, 49(2): 185--211

[16] Yuan Y R. The modified characteristic finite difference fractional steps method for nonlinear coupled system of multilayer fluid dynamics in porous media. Acta Mathematica Scientia, 2009, 29A(4): 858--872

[17] Ewing R E. Mathematical Modeling and Simulation of Multiphase Flow in Porous Media. Numerical Treatment of Multiphase Flows in Porous Media, Lecture Notes in Physics, Vol 552. New York: Springer-verlag, 2000: 43--57

[18] Yuan Y R, Han Y J. Numerical simulation of migration-accumulation of oil resources. Comput Geosi, 2008, 12: 153--162

[19] Yuan Y R, Han Y J. Numerical simulation and application of three-dimensional oil resources migration-accumulation of fluid
dynamics in porous media. Science in China, Series G, 2008, 51(8): 1144--1163

[20] Samarskii A A. Introduction to the Theory Difference Schemes. Moscow: Nauka, 1971 (Russion)

[21] Marchuk G I. Method of Numerical Mathematics. New York: Springer-Verlag, 1982

[22] Yanenko N N. The Method of Fractional Steps. New York: Springer-Verlag, 1971

[23] Yuan Y R. The characteristic finite difference fractional steps methods for compressible two-phase displacement problem.
Science in China, Series A, 1999, 42(1): 48--57

[24] Samarskii A A, Andreev B B. Finite Difference Methods for Elliptic Equation. Beijing: Science Press, 1984

[25] Yuan Y R. Characteristic finite difference method for moving boundary value problem of numerical simulation of oil deposit. Science in China, Series A, 1994, 37(12): 1442--1453

[26] Chen G N. Matrix Theory and Application. Beijing: Science Press, 2007

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

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

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Yonghong YAO, Olaniyi S. IYIOLA, Yekini SHEHU. THREE INERTIAL ACCELERATION ALGORITHMS FOR SOLVING NON-MONOTONE EQUILIBRIUM PROBLEMS IN HILBERT SPACES[J]. 数学物理学报(英文版), 2025, 45(4): 1674-1700.
[2]	Jinbao JIAN, Xianke TANG, Jianghua YIN, Xianzhen JIANG. AN INEXACT SYMMETRIC PROXIMAL ADMM WITH CONVEX COMBINATION PROXIMAL CENTERS FOR SEPARABLE CONVEX PROGRAMMING[J]. 数学物理学报(英文版), 2025, 45(4): 1701-1722.
[3]	Diancong JIN, Derui SHENG. ASYMPTOTICS OF LARGE DEVIATIONS OF FINITE DIFFERENCE METHOD FOR STOCHASTIC CAHN-HILLIARD EQUATION[J]. 数学物理学报(英文版), 2025, 45(3): 1078-1106.
[4]	Hongwu ZHANG, Yanhui LI. MODIFIED LANDWEBER ITERATIVE METHOD FOR A BACKWARD PROBLEM IN TIME OF THE DIFFUSION EQUATION WITH LOCAL AND NONLOCAL OPERATORS[J]. 数学物理学报(英文版), 2025, 45(3): 1205-1222.
[5]	Zhuang SHAN. MODIFIED INERTIAL SUBGRADIENT EXTRAGRADIENT METHODS FOR SOLVING A SUPPLY CHAIN NETWORK EQUILIBRIUM MODEL[J]. 数学物理学报(英文版), 2025, 45(3): 1223-1234.
[6]	Yirang YUAN, Changfeng LI, Huailing SONG, Tongjun SUN. A MIXED FINITE ELEMENT AND UPWIND MIXED FINITE ELEMENT MULTI-STEP METHOD FOR THE THREE-DIMENSIONAL POSITIVE SEMI-DEFINITE DARCY-FORCHHEIMER MISCIBLE DISPLACEMENT PROBLEM[J]. 数学物理学报(英文版), 2025, 45(2): 715-736.
[7]	Gonglin YUAN, Xiong ZHAO, Jiajia YU. GLOBAL CONVERGENCE OF A CAUTIOUS PROJECTION BFGS ALGORITHM FOR NONCONVEX PROBLEMS WITHOUT GRADIENT LIPSCHITZ CONTINUITY^*[J]. 数学物理学报(英文版), 2024, 44(5): 1735-1746.
[8]	Xiaoyu XIA, Litan YAN, Qing YANG. THE LONG TIME BEHAVIOR OF THE FRACTIONAL ORNSTEIN-UHLENBECK PROCESS WITH LINEAR SELF-REPELLING DRIFT[J]. 数学物理学报(英文版), 2024, 44(2): 671-685.
[9]	Xia Tao, Ziqing Xie. THE UNIFORM CONVERGENCE OF A DG METHOD FOR A SINGULARLY PERTURBED VOLTERRA INTEGRO-DIFFERENTIAL EQUATION^*[J]. 数学物理学报(英文版), 2023, 43(5): 2159-2178.
[10]	Xia YE, Yanxia XU, Zejia WANG. THE ZERO LIMIT OF THERMAL DIFFUSIVITY FOR THE 2D DENSITY-DEPENDENT BOUSSINESQ EQUATIONS^∗[J]. 数学物理学报(英文版), 2023, 43(4): 1800-1818.
[11]	Xueke Pu, Wenli Zhou. ON THE RIGOROUS MATHEMATICAL DERIVATION FOR THE VISCOUS PRIMITIVE EQUATIONS WITH DENSITY STRATIFICATION^*[J]. 数学物理学报(英文版), 2023, 43(3): 1081-1104.
[12]	Kunrada Kankam, Prasit Cholamjiak. DOUBLE INERTIAL PROXIMAL GRADIENT ALGORITHMS FOR CONVEX OPTIMIZATION PROBLEMS AND APPLICATIONS^*[J]. 数学物理学报(英文版), 2023, 43(3): 1462-1476.
[13]	Minghua Yang, Jinyi Sun, Zunwei Fu, Zheng Wang. THE SINGULAR CONVERGENCE OF A CHEMOTAXIS-FLUID SYSTEM MODELING CORAL FERTILIZATION^*[J]. 数学物理学报(英文版), 2023, 43(2): 492-504.
[14]	Ran Wang, Beibei Zhang. A LARGE DEVIATION PRINCIPLE FOR THE STOCHASTIC GENERALIZED GINZBURG-LANDAU EQUATION DRIVEN BY JUMP NOISE^*[J]. 数学物理学报(英文版), 2023, 43(2): 505-530.
[15]	Zhendong Fang, Ning Jiang. CONVERGENCE FROM THE TWO-SPECIES VLASOV-POISSON-BOLTZMANN SYSTEM TO THE TWO-FLUID INCOMPRESSIBLE NAVIER-STOKES-FOURIER-POISSON SYSTEM WITH OHM'S LAW^*[J]. 数学物理学报(英文版), 2023, 43(2): 777-820.