Journal of Computational and Applied Mathematics ( IF 2.1 ) Pub Date : 2021-03-20 , DOI: 10.1016/j.cam.2021.113521 Yi Qin , Yanren Hou , Wenlong Pei , Jian Li
This report considers a variable time-stepping algorithm proposed by Dahlquist, Liniger and Nevanlinna and discusses its application to the unsteady Stokes/Darcy model. Although long-time forgotten and little explored, the algorithm performs advantages in variable time-stepping analysis of various fluid flow systems, including the coupled Stokes/Darcy model. We first prove that the approximate solutions to the unsteady Stokes/Darcy model are unconditionally stable due to the -stability of the method. Then variable time-stepping error analysis follows from the combination of -stability and consistency of the method. Numerical experiments verify the theoretical results, demonstrating both accuracy and stability of the algorithm.
中文翻译:
非定常Stokes / Darcy模型的可变时步算法
本报告考虑了Dahlquist,Liniger和Nevanlinna提出的可变时步算法,并讨论了其在非定常Stokes / Darcy模型中的应用。尽管长期被遗忘并且很少被探索,但是该算法在各种流体流系统的可变时间步长分析中具有优势,包括耦合的Stokes / Darcy模型。我们首先证明了非定常Stokes / Darcy模型的近似解是无条件稳定的,这是由于-方法的稳定性。然后结合以下方法进行可变的时间步长误差分析-方法的稳定性和一致性。数值实验验证了理论结果,证明了算法的准确性和稳定性。