  This report considers a variable step time discretization algorithm proposed
by Dahlquist, Liniger and Nevanlinna and applies the algorithm to the unsteady
Stokes/Darcy model. Although long-time forgotten and little explored, the
algorithm performs advantages in variable timestep analysis of various fluid
flow systems, including the coupled Stokes/Darcy model. The paper proves that
the approximate solutions to the unsteady Stokes/Darcy model are
unconditionally stable due to the G-stability of the algorithm. Also variable
time stepping error analysis follows from the combination of G-stability and
consistency of the algorithm. Numerical experiments further verify the
theoretical results, demonstrating the accuracy and stability of the algorithm
for time-dependent Stokes/Darcy model.
