Modeling flow in geosystems with natural fault is a challenging problem due to low permeability of fault compared to its surrounding porous media. One way to predict the behavior of the flow while taking the effects of fault into account is to use the mixed finite element method. However, the mixed method could be time consuming due to large number of degree of freedom since both pressure and velocity are considered in the system. A new modeling method is presented in this paper. First, we introduce approximations of pressure based on the relation of pressure and velocity. We furthure decouple the approximated pressure from velocity so that it can be solved independently by continuous Galerkin finite element method. The new problem involves less degree of freedom than the mixed method for a given mesh . Moreover, local problem associated with a small subdomain around the fault is additionally solved to increase the accuracy of approximations around fault. Numerical experiments are conducted to examine the accuracy and efficiency of the new method. Results of three-dimensional tests show that our new method is up to 30$\times$ faster than the the mixed method at given $L^2$ pressure error.

中文翻译：

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一种模拟具有浸没断层的多孔介质流动的有效方法

由于与周围多孔介质相比，断层的渗透率较低，因此对具有天然断层的地质系统中的流动进行建模是一个具有挑战性的问题。在考虑故障影响的同时预测流动行为的一种方法是使用混合有限元方法。然而，由于在系统中同时考虑压力和速度，混合方法可能会因大量自由度而耗时。本文提出了一种新的建模方法。首先，我们根据压力和速度的关系介绍压力的近似值。我们进一步将近似压力与速度解耦，以便可以通过连续伽辽金有限元方法独立求解。与给定网格的混合方法相比，新问题涉及的自由度要小。而且，另外解决了与故障周围小子域相关的局部问题，以提高故障周围近似值的准确性。进行数值实验以检验新方法的准确性和效率。三维测试结果表明，在给定的 $L^2$ 压力误差下，我们的新方法比混合方法快 30$\times$。