Free surface and seepage flow rate determination under the bed of open channels using smoothed fixed grid finite element method

Free surface seepage flow problems in porous medias have many industrial and agricultural applications. In these problems, the geometric shape of the phreatic surface is unknown a priori and therefore the unconfined seepage problems are categorized as variable domain problems. Solving these problems using methods such as finite element method undergoes some difficulties because the domain boundary changes in each iteration and remeshing is inevitable. In the present paper, the smoothed fixed grid finite element method which is a new numerical approach based on non-boundary-fitted meshes is used to solve free surface seepage problems. The use of non-boundary-fitted meshes leads to simplification of solution of variable domain problems. In this method, gradient smoothing technique is used to formulate internal and boundary intersecting elements. To evaluate the applicability of the proposed method, some numerical examples are solved and the results are compared with those presented in the literature.