This paper first presents a first order ${\theta}$-scheme which is one parameter family of Linear Multistep Methods for the unsteady Stokes-Darcy model. Then, on the basis of this scheme, we use a time filter algorithm to increase the convergence order to the second order with almost no increasing the amount of computation, from which we get a new efficient algorithm. Finally, we theoretically analyze the stabilities and error estimations of coupled and decoupled schemes respectively, and we also do some numerical experiments to verify the effectiveness, convergence and efficiency.
翻译：本文首先展示了第一顺序 $ {theta} $- scheme, 这是不稳定的斯托克斯- 达西模型的线性多步方法的一个参数系列。 然后, 根据这个方案, 我们使用时间过滤算法将趋同顺序提高到第二顺序, 几乎不增加计算量, 我们从中可以得到一个新的高效算法。 最后, 我们从理论上分析了 组合和分离的方案的稳定性和误差估计, 我们还做了一些数字实验, 以验证效果、 趋同和效率 。
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