We consider the inverse problem of recovering the missing flux and concentration on some part of a boundary of an aquifer using overspecified measurements available on some accessible part. The aquifer is under the action of point-forces located inside the domain and governed by the advection-diffusion equation. The method used is based on a fictitious domain decomposition. Numerical tests are done attesting the performance of the identification process.
We consider fiber-reinforced composites, where the fibers present some distortion in their longitudinal direction. The length scale of this distorsion is much larger than the spacing of the fibers. We derive asymptotic formulas for a conduction problem. Reiterated homogenization, i.e. homogenizing with respect to the smallest length scale, then with respect to the largest does not capture the effects of distortion. Instead, we use a representation formula to show how distortion influences the correction terms.
The data completion method combined with the modeling of water flow and solute transport in saturated porous media is used twice to identify the extent of polluted water intrusion from the downstream boundary of an aquifer. The aim of this work is to solve the problem even though data are missing on some of the boundaries, by exploiting the fact that there are over specified data on the other boundaries. Indeed, it is assumed that the flow and the water head are known on the upstream boundary while the pollutant concentrations are known on the downstream boundary. The method developed in this work allows to determine the flows, water heads and pollutant concentrations in the whole domain. The method is applied in different aquifer configurations with pumping wells, the results are satisfactory. The model developed has shown its effectiveness in detecting the intrusion of polluted water and can be used in real cases.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.