Abstract
This paper discusses the analytic solutions of the diffusion equation for the movement of water in unsaturated soil. Firstly, according to the experience relation between the diffusivity “D(0)” and water content in soil “0”, and through variable substitution, the original diffusion equation is converted into the form easy to solve. Then, the variables separation method together with the Boltzmann transform method is used to find out the solution of the new partial differential equation. So the analytic function of 0(x, t) is obtained, which is verified by the experiment of water flow through unsaturated soil.
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References
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Communicated by Chen Zhenghan
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Hang, L., Zhiqiang, L. Almost analytic solutions and their tests of the horizontal diffusion equation for the movement of water in unsaturated soil. Appl Math Mech 18, 647–655 (1997). https://doi.org/10.1007/BF00127012
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DOI: https://doi.org/10.1007/BF00127012