Abstract
Flow and transport problems in porous media are well-known for their high computational cost. In the far field simulation of an underground nuclear waste disposal site, one has to work with extremely different length and time scales, and highly variable coefficients while satisfying strict accuracy requirements. One strategy for tackling these difficulties is to apply a non-overlapping domain decomposition method which allows local adaptation in both space and time and makes possible the use of parallel algorithms. The substructuring method with a Steklov Poincare operator, which is widely used by engineers for steady problems with strong heterogeneities, is a promising option. The optimized Schwarz waveform relaxation (OSWR) method, which has been developed over the last decade for finite element and finite volume methods, is another potential choice.
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