摘 要 本文针对一类描述多孔介质中多相流的非线性扩散方程，提出了一种隐式有限差分法。该方法对非线性扩散项进行隐式处理，因此每个时间步上的非线性待求系统由比卡迭代法进行求解。数值模拟的结果显示隐式有限差分法是一种有效稳定的算法。

关键词 数值模拟；多孔介质；多相流；隐式有限差分法

0 Introduction
The fast and accurate flow simulations on multiple plausible geological models on a routinely basis are required by the increased demands for assessment of uncertainties and history matching in recent years. This requirement can not be fulfilled by the conventional reservoir simulators, and therefore there seems a trend within the petroleum industry to simulate reduced sets of equations[1-2]. Oil reservoir simulation based on these reduced sets of equations has many important applications in areas such as oil and gas exploration, management of petroleum reservoirs. We can easily select, for example, the type of the recovery method, fluid production, injection rates and well locations with its help.
In this paper, we consider a kind of nonlinear diffusion equation, which is closely relevant to multiphase porous media flow, and put forward an implicit finite-difference algorithm. In this algorithm, the nonlinear system that needs to be solved for each time level can be solved by the Picard iteration[3] because of the implicit treatment of the nonlinear diffusion term. The synthetic examples demonstrate that our algorithm is effective and stable.
作者：何欢欢