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.

开发了一种多维质量保守数值方法，特别适用于有限的计算资源，用于解决瞬态变饱和地下水流动问题。Richards 方程使用有限元方法在空间上离散，在时间上使用隐式欧拉方案进行离散，其中使用质量守恒和质量集总技术来保持数值模拟的稳定。此外，所涉及的刚度和质量矩阵以某种方式进行近似以保证较少的计算工作量。为了确认此代码的准确性和效率，我们使用使用一维、二维和三维问题的基准测试对其进行了验证。本模型还应用于实际现场案例问题，其中清楚地证明了其优越性。该代码对每个问题都取得了可靠的结果。