An extended mesh deformation algorithm for solving free surface problems
F.X. Liu, G.H. Lei, Hongwei Lin · 2023
The finite-element mesh deformation technique is one of the iterative solution methods used to locate the free surfaces in unconfined seepage flows through dams or levees. This technique involves adjusting the element heights and, hence, moving the top boundary of the mesh to the computed free surface as the iterations proceed. Smith et al. (2014) proposed an algorithm and program to adjust the element heights. In order to alleviate element distortion and improve numerical stability, Fenton & Griffiths (1997) proposed an additional algorithm and program to adjust the element widths. Nevertheless, these algorithms and programs have been specialized to the elements above the downstream water level. In this paper, the two algorithms are extended to the elements below the downstream water level. The validity of the extended algorithm is demonstrated by comparisons with results of an analytical solution, a closed-form approximate solution, and a numerical study with a commercial software.