气藏两相渗流问题全隐式模拟的改进Newton方法及其数值比较

计算物理 ›› 1991, Vol. 8 ›› Issue (3): 271-278.

气藏两相渗流问题全隐式模拟的改进Newton方法及其数值比较

林刚¹, 石济民¹, 林振宝¹, 吕涛², 林爱民²

1. 香港理工学院数学系;
2. 中国科学院成都分院数理室, 成都 610015

收稿日期:1990-09-25 修回日期:1991-03-08 出版日期:1991-09-25 发布日期:1991-09-25

A MODIFIED NEWTON'S METHOD FOR FULLY IMPLICIT DIFFERENCE SCHEMES OF GAS RESERVIORS SIMULATION AND NUMERICAL COMPARISON OF RESULTS

Lin gang¹, Shi Jimin¹, Lin Zhengbao¹, Lü Tao², Lin Aimin²

1. Department of Mathematics Hong Kong Polytechnical Institute;
2. Institute of Mathematical Sciences Chengdu Branch, Academia Sinica, Chengdu

Received:1990-09-25 Revised:1991-03-08 Online:1991-09-25 Published:1991-09-25

摘要/Abstract

摘要： 本文分析含水气藏全隐式数值模似的计算问题,阐述了数值解偏微分方程的各种改进牛顿法,数值计算结果表明:采用萨曼斯基技巧改进牛顿方法可以提高气藏模拟的效率。

关键词: 气藏数值模拟, 全隐式格式, 改进牛顿法

Abstract: The numerical simulation of oil (gas) reservoirs can be described by two-phase penetration dynamic equations, which are high-dimensional, non-linear, singular and time-dependent partial differential equations, subjected to some appropriate initial and boundary conditions.The partial differential equations are discretized by differencing schemes (such as Fully Implicit method, 1MPES,etc.)and produce different non-linear algebraic systems.To solve a non-linear system Newton's method is the most popular method. But it requires calculation of a Jacobi matrix and solving a linear system in each iteration.These will consume huge computing CPU time.For saving the CPU time we have modified the Newton's method with Samanskii's idea and controled the number of iterations in solving the linear systems. The programming is quite simple. We tested our algorithm in a set of ideal data.The results are as accurate as those obtained from the Newton's method and the efficiency is better.

Key words: numerical simulation of gas reservoirs, fully implicit difference schemes, modified Newton's method

林刚, 石济民, 林振宝, 吕涛, 林爱民. 气藏两相渗流问题全隐式模拟的改进Newton方法及其数值比较[J]. 计算物理, 1991, 8(3): 271-278.

Lin gang, Shi Jimin, Lin Zhengbao, Lü Tao, Lin Aimin. A MODIFIED NEWTON'S METHOD FOR FULLY IMPLICIT DIFFERENCE SCHEMES OF GAS RESERVIORS SIMULATION AND NUMERICAL COMPARISON OF RESULTS[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1991, 8(3): 271-278.