Comparison of monolithic and splitting solution schemes for dynamic porous media problems

Proceeding from the governing equations describing a saturated poroelastic material with intrinsically incompressible solid and fluid constituents, we compare the monolithic and splitting solution of the different multi-field formulations feasible in porous media dynamics. Because of the inherent solid fluid momentum interactions, one is concerned with the class of volumetrically coupled problems involving a potentially strong coupling of the momentum equations and the algebraic incompressibility constraint. Here, the resulting set of differential-algebraic equations (DAE) is solved by the finite element method (FEN) following two different strategies: (1) an implicit monolithic approach, where the equations are first discretized in space using stable mixed finite elements and second in time using stiffly accurate implicit time integrators; (2) a semi-explicit implicit splitting scheme in the sense of a fractional-step method, where the DAE are first discretized in time, split using intermediate variables, and then discretized in space using linear equal-order approximations for all primary unknowns. Finally, a one- and a two-dimensional wave propagation example serve to reveal the pros and cons in regard to accuracy and stability of both solution strategies. Therefore, several test cases differing in the used multi-field formulation, the monolithic time-stepping method, and the approximation order of the individual unknowns are analyzed for varying degrees of coupling controlled by the permeability parameter. In the end, we provide a reliable recommendation which of the presented strategies and formulations is the most suitable for which particular dynamic porous media problem. Copyright (C) 2009 John Wiley & Sons, Ltd.