Robust and reliable numerical models are vital to solve the Richards’ equation, which depicts the variably saturated flows in porous media. In this study, the Richards’ equation is discretized spatially with the numerical manifold method (NMM) and temporally with the backward Euler scheme, in which the under-relaxation and mass lumping techniques are introduced to keep the numerical stability and mass balance. Several examples are performed to validate the correctness and accuracy of the proposed model. The numerical results demonstrate the potential applicability of the proposed model to solve saturated-unsaturated seepage problems.

中文翻译：

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使用数值流形法模拟多孔介质中的可变饱和流


稳健可靠的数值模型对于求解 Richards 方程至关重要，Richards 方程描述了多孔介质中可变饱和流动。在本研究中，Richards 方程使用数值流形法 （NMM） 在空间上离散，在时间上使用反向欧拉方案离散，其中引入了欠弛豫和质量集总技术以保持数值稳定性和质量平衡。执行了几个示例来验证所提出模型的正确性和准确性。数值结果表明，所提模型在解决饱和-非饱和渗流问题方面具有潜在的适用性。