Efficient mass conservative numerical model for solving variably saturated groundwater flow

A multi-dimensional mass conservative numerical method, particularly suitable for limited computational resources, is developed for solving transient variably saturated groundwater flow problems. The Richards equation is discretized spatially with a finite element method and temporally with an implicit Euler scheme, in which mass-conservative and mass-lumping techniques are used to keep the numerical simulation stable. In addition, the stiffness and mass matrices involved are approximated in a way to guarantee less computational effort. To confirm the accuracy and the efficiency of this code, we verified it using benchmark tests using one, two and three-dimensional problems. The present model is also applied to a real field case problem, where its superiority is clearly demonstrated. The code achieved reliable results for each problem.

Automated summary

The multi-dimensional mass conservative numerical method is developed for solving transient variably saturated groundwater flow problems, which is particularly suitable for limited computational resources. The method discretizes the Richards equation spatially with a finite element method and temporally with an implicit Euler scheme, using mass-conservative and mass-lumping techniques to ensure stability. The method also approximates stiffness and mass matrices to reduce computational effort, achieving reliable results in benchmark tests and real field case problems.