An Adaptive Time Filter Algorithm for the 2D/3D Unsteady Triple‐Porosity Stokes Model Arising in Super‐Hydrophobic Proppant Modification in Hydraulic Fracturing Systems

ABSTRACT In this paper, we propose an adaptive time filter algorithm for the 2D/3D unsteady triple‐porosity Stokes model arising in super‐hydrophobic proppant modification in hydraulic fracturing systems. The time filter algorithm with variable time steps is given, which can improve the time accuracy from the first order to the second order without increasing any computational complexity. Moreover, this adaptive decoupled algorithm can reduce calculational costs and provide effective error control for its solution, compared to traditional numerical algorithms. Especially, the stability and second‐order convergence of the time filter algorithm with variable time steps are proven under a relaxed time step restriction of the form . Numerical results confirm the results of our theoretical analysis and the complex flow characteristics of the model through 2D/3D numerical examples.