Parallel non-iterative methods for evolutionary semilinear flow problems

This paper deals with the efficient numerical Solution of semilinear parabolic problems that describe flow phenomena through non-isotropic porous media. For the time integration of such problems, we propose a linearly implicit fractional step method that considers function and operator splittings related to suitable decompositions of the flow domain. The resulting family of elliptic problems is discretized in space by means of the support-operator technique, obtaining a nine-cell finite difference scheme on a logically rectangular grid. Owing to the chosen splittings, the totally discrete scheme involves sets of uncoupled linear systems that can be solved in parallel. Finally, a numerical experiment is included in order to show the unconditionally convergent behaviour of the scheme. Copyright (C) 2007 John Wiley & Sons, Ltd.