The conservative splitting domain decomposition method for multicomponent contamination flows in porous media. (English) Zbl 1453.65305

Summary: In the paper, a new conservative splitting decomposition method (S-DDM) is developed for computing nonlinear multicomponent contamination flows in porous media over multi-block sub-domains. On each block-divided sub-domain, we take three steps to solve the coupled nonlinear system of water-head equation and multicomponent concentration equations in each time interval. The interface Darcy’s velocity and the interface global concentration fluxes are first predicted by the semi-implicit flux schemes, while the solutions of water-head and multicomponent concentrations, Darcy’s velocity and global concentration fluxes in the interiors of sub-domains are computed by one-directional splitting implicit solution-flux coupled schemes on staggered meshes, and finally the interface Darcy velocity and global concentration fluxes are corrected by the interior solutions. The significance of our scheme is that while it keeps the advantages of the non-overlapping domain decomposition and the splitting technique, it preserves mass on the whole domain of domain decompositions. Numerical experiments are presented to illustrate the excellent performance of our proposed conservative S-DDM approach for computing nonlinear multicomponent contamination flows in groundwater. The developed algorithm of the conservative S-DDM works efficiently over multiple block-divided sub-domains, which can be applied in simulation of large scale multicomponent contamination flows in parallel computing.


65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
76S05 Flows in porous media; filtration; seepage
76T06 Liquid-liquid two component flows
86A05 Hydrology, hydrography, oceanography
76T30 Three or more component flows
76V05 Reaction effects in flows


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