Isogeometric analysis in solution of unconfined seepage problems

Abstract This article investigates the numerical solution of saturated unconfined seepage problems in which a fluid with a free surface passes through a porous media. In such cases, the geometry of the wet region is unknown in advance and must be obtained through an iterative process. Such problems are known as variable domain problems. Since the use of traditional mesh based numerical methods is not straight forward due to remeshing difficulties, the isogeometric analysis is proposed here which eliminates the meshing process and accordingly makes this method an attractive tool to deal with such problems. On the other hand, the use of isogeometric analysis accounts for other difficulties which this paper aims to address. In the isogeometric analysis the boundary control points are not located on the domain boundary. Therefore, in this article, a new boundary updating formula is proposed to reconstruct the free surface. For modifying the control net, the transfinite interpolation is used in order to update the control net when the geometry undergoes any change. The domain is considered inhomogeneous with spatially varied permeability. Three benchmark examples are solved to demonstrate the applicability of the proposed method. Finally, the results are compared with those available in the literature.