论文标题
一种有效的方法，用于在多孔培养基中进行浸入故障的流动
An efficient method for modeling flow in porous media with immersed faults
论文作者
论文摘要
与周围的多孔培养基相比，由于故障的渗透性较低，具有自然断层的地理系统的建模流量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。但是，由于系统在系统中都考虑了压力和速度，因此混合的方法可能是由于大量自由度而耗时的。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引入压力近似值。我们促进了速度的近似压力，以便可以通过连续的Galerkin有限元方法独立地求解。与给定网格的混合方法相比，新问题涉及的自由度少。此外，与周围的小子域相关的局部问题还可以解决，以提高断层周围近似值的准确性。进行数值实验以检查新方法的准确性和效率。三维测试的结果表明，我们的新方法比给定的$ l^2 $压力错误的混合方法快30美元$ \ times $。
Modeling flow in geosystems with natural fault is a challenging problem due to low permeability of fault compared to its surrounding porous media. One way to predict the behavior of the flow while taking the effects of fault into account is to use the mixed finite element method. However, the mixed method could be time consuming due to large number of degree of freedom since both pressure and velocity are considered in the system. A new modeling method is presented in this paper. First, we introduce approximations of pressure based on the relation of pressure and velocity. We furthure decouple the approximated pressure from velocity so that it can be solved independently by continuous Galerkin finite element method. The new problem involves less degree of freedom than the mixed method for a given mesh . Moreover, local problem associated with a small subdomain around the fault is additionally solved to increase the accuracy of approximations around fault. Numerical experiments are conducted to examine the accuracy and efficiency of the new method. Results of three-dimensional tests show that our new method is up to 30$\times$ faster than the the mixed method at given $L^2$ pressure error.
