Abstract:
The coupling of a free flow with a flow through porous media has
many potential applications in several fields related with computational science
and engineering, such as blood flows, environmental problems or food technolo gies. We present a reduced basis method for such coupled problems. The re duced basis method is a model order reduction method applied in the context of
parametrized systems. Our approach is based on a heterogeneous domain decompo sition formulation, namely the Stokes-Darcy problem. Thanks to an offline/online decomposition, computational times can be drastically reduced. At the same time
the induced error can be bounded by fast evaluable a-posteriori error bounds. In
the offline-phase the proposed algorithms make use of the decomposed problem
structure. Rigorous a-posteriori error bounds are developed, indicating the accu racy of certain lifting operators used in the offline-phase as well as the accuracy
of the reduced coupled system. Also, a strategy separately bounding pressure and
velocity errors is extended. Numerical experiments dealing with groundwater flow
scenarios demonstrate the efficiency of the approach as well as the limitations
regarding a-posteriori error estimation
