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<p>In soil water infiltration problems, the basic control equation, i.e., Richards equation is a nonlinear partial differential equation (PDE), and is difficult to solve. In this study, a finite difference lattice Boltzmann method (FDLBM), in which the D1Q5 model is employed as the lattice layout scheme, is developed to solve the 1-D Richards equation with water content as the main variable in unsaturated soil. The relationship between the lattice Boltzmann equation (LBE) and the Richards equation is established using a multiscale expansion technique. Numerical examples show that LBM is suitable to solve Richards equation in unsaturated soil water infiltration problems.</p>

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A finite difference lattice Boltzmann method for Richards equation in vertical unsaturated soil water infiltration

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Zhe Zhang,
  • He-fang Jing,
  • Qiu-tong Chen,
  • Yu-jie Yang

摘要

In soil water infiltration problems, the basic control equation, i.e., Richards equation is a nonlinear partial differential equation (PDE), and is difficult to solve. In this study, a finite difference lattice Boltzmann method (FDLBM), in which the D1Q5 model is employed as the lattice layout scheme, is developed to solve the 1-D Richards equation with water content as the main variable in unsaturated soil. The relationship between the lattice Boltzmann equation (LBE) and the Richards equation is established using a multiscale expansion technique. Numerical examples show that LBM is suitable to solve Richards equation in unsaturated soil water infiltration problems.