近几十年来，研究不可压缩流与多孔介质流耦合问题最广泛使用的 Stokes/Darcy 模型或 Navier-Stokes/Darcy 模型无论在理论分析方面还是在数值模拟方面都受到极大关注。为了弥补现有数值算法不稳定、低效率及高成本等不足，本项目拟针对该耦合模型的高效数值算法进行研究。首先，针对高阶算法高成本的问题，本项目考虑利用简单的Time Filters格式在几乎不增加额外消耗的情况下，将低阶算法的精度提高，从而降低成本；其次，针对算法低效率的情况，我们将利用变时间步长的DLN算法与时间自适应算法相结合以提高计算效率；最后，针对耦合算法计算规模大及不易编程实现的缺点，考虑将双自适应人工压缩分离算法应用于不可压缩流与多孔介质流耦合模型，利用解耦以及双自适应节省大量计算时间。本项目的研究内容是偏微分方程数值计算中的难点及重点，将对计算流体力学领域的研究起到重要推动作用。

In recent decades, Stokes/Darcy model and Navier-Stokes/Darcy model which are the most widely used to study the coupling problem of incompressible flow and porous media flow have attracted great attention both in theoretical analysis and numerical simulation. In order to make up for the instability, low efficiency and high cost of the existing numerical algorithms, this project intends to conduct research on the efficient numerical algorithms of the coupled model. First of all, aiming at the problem of high cost of higher-order algorithms, this project considers to improve the precision of lower-order algorithms and reduce the cost by using simple Time Filters scheme with almost no additional consumption. Secondly, in view of the low efficiency of the algorithm, we will combine the variable time step DLN algorithm with the time adaptive algorithm to improve the computational efficiency. Finally, considering the large scale of coupling algorithm and its difficulty in programming, the double adaptive artificial compression separation algorithm is considered to be applied to the coupled model of incompressible flow and porous media flow, and the decoupled and double adaptive algorithm can save a lot of computation time. The research content of this project is the difficulty and key points in the numerical calculation of partial differential equations, which will play an important role in promoting the research in the field of computational fluid dynamics.