论文标题
分析不稳定的Stokes/Darcy模型的新的自适应时间过滤算法
Analysis of A New Adaptive Time Filter Algorithm for The Unsteady Stokes/Darcy Model
论文作者
论文摘要
在本报告中，我们为Unsteady Stokes/Darcy模型提出了一种新的自适应时间过滤算法。首先，我们提出一个带有可变时间步长的一阶$θ$ -Scheme，它是线性多步法方法的一个参数家族，并使用时间过滤器算法将收敛顺序提高到二阶，而几乎没有增加计算量。此外，我们构建了耦合和解耦的自适应算法。然后，我们分别分析了线性多步方法和时间过滤器的可变时间步长算法的稳定性和二阶精度。最后，我们使用两个数值实验来验证理论结果，包括使用自适应方法的有效性，收敛性和效率。
In this report, we propose a new adaptive time filter algorithm for the unsteady Stokes/Darcy model. First we present a first order $θ$-scheme with the variable time step which is one parameter family of Linear Multi-step methods and use a time filter algorithm to increase the convergence order to second order with almost no increasing the amount of computation. Furthermore, we construct coupled and decoupled adaptive algorithms. Then we analyze stabilities and the second-order accuracy of variable time-stepping algorithm for Linear Multi-step methods plus time filter, respectively. Finally, we use two numerical experiments to verify theoretical results including effectiveness, convergence and efficiency with adaptive method.
