Selection criteria of mesh size and time step in FEM analysis of highly nonlinear unsaturated seepage process

The selection criteria of the mesh size and time step that ensures a convergent result in FEM analysis of highly nonlinear unsaturated seepage process is established. First, the concept of critical mesh size (L-c) and critical time step (delta t(c)) are theoretically deduced, and their framework is set up. Subsequently, formulas for the prediction of L-c and delta t(c) are proposed through a series of numerical experiments. Additionally, the reliability of the proposed criteria is verified by analytical solutions, model test results, and quasi-engineering problems, respectively. Finally, the ranges of L-c and delta t(c) under various conditions in engineering applications are recommended. The results show that the proposed criteria can predict the approximate range of L-c and delta t(c), so as to obtain the convergent wetting front position and water content distribution. In addition, the criteria can be applied to the scale and dimensions of laboratory experiments and engineering cases. Moreover, the mesh size and time step were interdependent. Under limiting conditions, the appropriate mesh size should be selected prior to the time step. The research results can provide a reference for improving the accuracy of the FEM analysis of unsaturated seepage.

Automated summary

This study establishes the selection criteria for the mesh size and time step in FEM analysis of highly nonlinear unsaturated seepage processes, ensuring convergence of results. Through theoretical deduction and numerical experiments, critical mesh size and critical time step are defined and their prediction formulas are proposed. The reliability of the criteria is verified through analytical solutions, model tests, and engineering problems. The study provides recommended ranges for the mesh size and time step in engineering applications, allowing for the convergence of wetting front position and water content distribution.