Comparison of finite difference schemes for water flow in unsaturated soils

Taheri Shahraiyni, H ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. Publisher: 2009
  3. Abstract:
  4. Flow movement in unsaturated soil can be expressed by a partial differential equation, named Richards equation. The objective of this study is the finding of an appropriate implicit numerical solution for head based Richards equation. Some of the well known finite difference schemes (fully implicit, Crank Nicolson and Runge-Kutta) have been utilized in this study. In addition, the effects of different approximations of moisture capacity function, convergence criteria and time stepping methods were evaluated. Two different infiltration problems were solved to investigate the performance of different schemes. These problems include of vertical water flow in a wet and very dry soils. The numerical solutions of two problems were compared using four evaluation criteria and the results of comparisons showed that fully implicit scheme is better than the other schemes. In addition, utilizing of standard chord slope method for approximation of moisture capacity function, automatic time stepping method and difference between two successive iterations as convergence criterion in the fully implicit scheme can lead to better and more reliable results for simulation of fluid movement in different unsaturated soils
  5. Keywords:
  6. Crank-Nicolson ; Finite difference methods ; Fully implicit ; Richards equation ; Runge-Kutta ; Convergence criterion ; Dry soil ; Evaluation criteria ; Finite difference scheme ; Fluid movement ; Fully implicit scheme ; Moisture capacity ; Numerical solution ; Slope method ; Successive iteration ; Time stepping method ; Unsaturated soil ; Water flows ; Difference equations ; Finite difference method ; Flow of water ; Hydraulics ; Moisture ; Partial differential equations ; Soils ; Solute transport ; Runge Kutta methods
  7. Source: World Academy of Science, Engineering and Technology ; Volume 40 , 2009 , Pages 21-25 ; 2010376X (ISSN)
  8. URL: http://citeseerx.ist.psu.edu/viewdoc/download?doi=