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In this report, we propose a new adaptive time filter algorithm for theunsteady Stokes/Darcy model. First we present a first order ${\theta}$-schemewith the variable time step which is one parameter family of Linear Multi-stepmethods and use a time filter algorithm to increase the convergence order tosecond order with almost no increasing the amount of computation. Furthermore,we construct coupled and decoupled adaptive algorithms. Then we analyzestabilities and the second-order accuracy of variable time-stepping algorithmfor Linear Multi-step methods plus time filter, respectively. Finally, we usetwo numerical experiments to verify theoretical results includingeffectiveness, convergence and efficiency with adaptive method.

Analysis of A New Adaptive Time Filter Algorithm for The Unsteady Stokes/Darcy Model