A variable time-stepping algorithm for the unsteady Stokes/Darcy model

Abstract 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 G -stability of the method. Then variable time-stepping error analysis follows from the combination of G -stability and consistency of the method. Numerical experiments verify the theoretical results, demonstrating both accuracy and stability of the algorithm.