Efficient and long time stable IMEX schemes for the unsteady dual-porosity-Stokes system

Abstract

In this paper, we introduce an efficient and long time stable implicit–explicit(IMEX) scheme for the dual-porosity-Stokes equations. On the basis of backward Euler scheme and the solution at previous time level, we apply implicit discretization for sub-problems terms and explicit discretization for interface terms. By introducing a new scalar auxiliary variable (SAV), the scheme avoids time step constraints in long time stability analysis. We derive the error estimates of the full discretization with finite element method for the spatial discretization without any time step conditions. Moreover, we extend the approach to higher order IMEX schemes and develop variable time stepsize adaptive algorithm using time filter. Numerical tests are provided to validate the accuracy of several numerical schemes and assess industrial applicability of the coupled model in the multistage fractured horizontal wellbore problem.