In this study, we focus on the modelling of infiltration process in porous media. We use the meshless techniques for efficiently solving the Richards equation which describes unsaturated water flow through soils. The design of approximate numerical methods for the Richards equation remains computationally challenging and requires the development of efficient numerical techniques. This difficulty is mainly due to the nonlinearity of the unsaturated hydraulic conductivity and the capillary pressure function. In this study, we develop a new method based on the localized radial basis function (RBF) and the Kirchhoff transformation technique in order to solve Richards equation in one and two-dimensional homogeneous medium. Our approach using the multiquadric radial basis function allows us to reduce the computational time and provide accurate numerical solutions. The proposed method does not require mesh generation. Picard's iterations are used to linearize the resulting nonlinear problem obtained using the Kirchhoff transformation technique. The numerical simulations show the capability of the proposed numerical techniques in predicting the dynamics of water through unsaturated soils.
翻译:在此研究中,我们侧重于以多孔介质的渗透过程建模。 我们使用无网点技术有效解决Richards 等式,该等式描述了不饱和的土壤水流。 设计理查斯等式的近似数字方法在计算上仍然具有挑战性, 需要开发高效的数字技术。 这个困难主要是由于不饱和的液态传导性和毛虫压力函数的不线性。 在这个研究中, 我们根据局部的辐射基函数( RBF) 和 Kirchhoff 变异技术开发了一种新的方法, 以便用一二维同质介质介质解理查斯等式。 我们使用多孔线基函数的方法可以减少计算时间, 并提供准确的数字解决方案。 拟议的方法不需要 mesh 生成。 Picard 的迭代法被用来将由此产生的非线性问题通过 Kirchhoff 变换技术线化。 数字模拟显示拟议的数字技术通过不饱和土壤预测水的动态的能力。