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This paper is concerned with the numerical solution of compressible fluidflow in a fractured porous medium. The fracture represents a fast pathway(i.e., with high permeability) and is modeled as a hypersurface embedded in theporous medium. We aim to develop fast-convergent and accurate global-in-timedomain decomposition (DD) methods for such a reduced fracture model, in whichsmaller time step sizes in the fracture can be coupled with larger time stepsizes in the subdomains. Using the pressure continuity equation and thetangential PDEs in the fracture-interface as transmission conditions, threedifferent DD formulations are derived; each method leads to a space-timeinterface problem which is solved iteratively and globally in time. Efficientpreconditioners are designed to accelerate the convergence of the iterativemethods while preserving the accuracy in time with nonconforming grids.Numerical results for two-dimensional problems with non-immersed and partiallyimmersed fractures are presented to show the improved performance of theproposed methods.

Fast and accurate domain decomposition methods for reduced fracture models with nonconforming time grids