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Finite analytic method for modeling variably saturated flows.

Zaiyong Zhang1, Wenke Wang2, Chengcheng Gong2

  • 1Key Laboratory of Subsurface Hydrology and Ecological Effects in Arid Region, Chang'an University, Ministry of Education, PR China; School of Environmental Science and Engineering, Chang'an University, PR China; Department of Hydrology and Water Resources, University of Arizona, Tucson, AZ 85721, USA.

The Science of the Total Environment
|November 18, 2017
PubMed
Summary
This summary is machine-generated.

A new finite analytic method (FAM) accurately and efficiently solves Richards

Keywords:
Finite analytic methodKirchhoff transformationRichards' equationVariably saturated flow

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Area of Science:

  • Environmental science
  • Computational mathematics
  • Soil physics

Background:

  • Richards' equation models unsaturated flow in porous media.
  • Numerical methods often struggle with oscillations and dispersion.
  • Accurate modeling is crucial for water resource management.

Purpose of the Study:

  • To develop a novel finite analytic method (FAM) for solving the 2D Richards' equation.
  • To enhance numerical stability and reduce dispersion in unsaturated flow simulations.
  • To provide a reliable computational tool for soil water movement.

Main Methods:

  • Developed a finite analytic method (FAM) integrating analytic solutions into local elements.
  • Formulated an algebraic representation of the partial differential equation for unsaturated flow.
  • Verified the FAM model against analytical solutions, VSAFT2, and field data.

Main Results:

  • The FAM effectively controlled numerical oscillation and dispersion.
  • Numerical solutions from FAM demonstrated high accuracy.
  • The method proved to be computationally efficient compared to alternatives.

Conclusions:

  • The finite analytic method is a robust and efficient approach for 2D Richards' equation.
  • FAM offers improved accuracy and stability for unsaturated flow modeling.
  • This method has potential applications in hydrology and environmental engineering.