Free surface flow through rock-fill dams analyzed by FEM with level set approach

Abstract

A stabilized-finite element formulation is coupled with a level set technique for computations of incompressible non-linear flow with interfaces between two immiscible fluids. An interface capturing formulation (ICF) for non-linear, free surface, seepage flow in rock-fill dams is proposed. The formulation is derived for two- and three-dimensional flow within a fixed mesh domain. The resulting formulation is general and applicable for various steady and transient two-phase flow problems. FE-refinement is processed for the entire fixed mesh domains. A general solver is also reviewed for large and non-symmetric non-positive definite linear system of equations with the GMRES-update technique based on a Newton-iterative method. The computational procedure has been implemented in MATLAB. A comparison is performed between the 2-D computed test problem for coarse and refined meshes together with some proposed analytical solutions for nonlinear seepage flow with free surface in rock-fill dams. An expansion of the 2-D program code to a 3-D one for a rectangular rock-fill dam is also developed and simulated in MATLAB. The performance of the computations in 3-D is very promising and its opening the future for possible industrial applications using the same simple technique. Computations for a simple 3-D seepage flow problem with free surface in rock-fill dam are included in present paper. A general mesh generator and solver for large scale and complex 3-D flow problems in a real embankment dam is also under construction in C++.