Adaptive Modeling for free-surface flowm


MOX 48
Adaptive Modeling for free-surface flowm
Wednesday 20th October 2004
Perotto, Simona
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This work represents a first step towards the adaptive simulation of the motion of water in a complex hydrodynamic configuration, such as a channel network or a river delta by means of different mathematical models. A wide spectrum of space and time scales is involved due to the presence of physical phenomena of different nature. Ideally, moving from a hierarchy of hydrodynamic models, one should solve the most complex model (with solution u_fine) to accurately describe all the physical features of the problems at hand. In more detail, for a user-defined output functional F, we aim to approximate, within a prescribed tolerance (), the value F (u_fine) by means of the quantity F (u_adapted), u_adapted being the adapted solution confining the most complex model only on a restricted region of the computational domain. We aim to provide an efficient tool able to automatically select regions of the domain where to solve the coarse hydrodynamic model rather than the finer one, while guaranteeing |F(u_fine)F (u_adapted)| below the tolerance (). This goal is achieved via a suitable a posteriori modeling error analysis developed in the framework of a goal-oriented theory. We extend the dual-based approach provided in [3] for steady equations to the case of a generic time-dependent problem. Then this analysis is particularized to the case of free-surface flows. In the last part of the paper an exhaustive numerical validation is carried out, while emphasizing the crucial matter of the time discretization for the dual problem.
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Perotto, S., Adaptive modeling for free-surface flows, M2AN Math. Model. Numer. Anal., 40 (2006), no. 3, 469-499