Comparison of Finite Difference Schemes for Fluid Flow in Unsaturated Porous Medium (Soil)

Authors

  • Ramesh Chandra Timsina Department of Mathematics, Patan Multiple Campus, Tribhuvan University, Kathmandu, Nepal
  • Kedar Nath Uprety Central Department of Mathematics, Tribhuvan University, Kathmandu, Nepal

DOI:

https://doi.org/10.3126/nmsr.v39i1.46915

Keywords:

Finite Difference Methods, Richards Equation, Kirchho Transformation, Super Time-Stepping Schemes, infiltration

Abstract

Water movement in an unsaturated porous medium (soil) can be expressed by Richards equation with the mass conservation law and Darcy-Buckingham's law. This equation can be expressed in three different forms as pressure head-based, moisture content based and mixed from. In this study, we solve one dimensional Richards Equation in mixed form numerically using finite difference method with various time-stepping schemes: Forward Euler, Backward Euler, Crank-Nicolson and a Stabilized Runge-Kutta-Legendre Super Time-Stepping and we compare their performances using Dirichlet boundary condition on an isotropic homogeneous vertical soil column.

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Published

2022-07-27

How to Cite

Timsina, R. C., & Uprety, K. N. (2022). Comparison of Finite Difference Schemes for Fluid Flow in Unsaturated Porous Medium (Soil). The Nepali Mathematical Sciences Report, 39(1), 22–35. https://doi.org/10.3126/nmsr.v39i1.46915

Issue

Vol. 39 No. 1 (2022)

Section

Articles

License

Copyright © The Nepali Mathematical Sciences Report