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

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

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。

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 .