一种求解Muskat问题的有限元-有限差分算法

A FINITE ELEMENT-FINITE DIFFERENCE SCHEME FOR SOLVING MUSKAT PROBLEM

本文采用有限元一有限差分算法,首次计算了Muskat问题的弱形式。这种算法的特点是交替求解压力和饱和度,用有限元法解压力方程,用有限差分法解饱和度方程,有限元网格与有限差分网格融为一体,网格随油水界面的推进而浮动。将本文算法的结果与解析解及传统数值模拟解进行了比较,比较的结果令人满意。

The weak form of the Muskat problem is considered in this paper. A finite-element finite difference scheme is proposed for solving the Muskat problem. Pressure andsaturation values are calculated alternatively. Pressure profile is computed by finite elementmethod and saturation distribution by finite difference method. The nodes of finite element grid are in agreement with the nodes of finite difference grid. The grids vary withmovement of the water-oil displacement front. The numerical solution is compared withthe analytical solution and the solution of conventional numerical, simulation method. Theresults of comparison are satisfactory.