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Stability Analysis of the Explicit Difference Scheme for Richards Equation
Fengnan Liu1, Yasuhide Fukumoto2, Xiaopeng Zhao3
1School of Mathematical and Physical Sciences, Dalian University of Technology, Panjin 124221, China.
Abstract:
A stable explicit difference scheme, which is based on forward Euler format, is proposed for the Richards equation. To avoid the degeneracy of the Richards equation, we add a perturbation to the functional coefficient of the parabolic term. In addition, we introduce an extra term in the difference scheme which is used to relax the time step restriction for improving the stability condition. With the augmented terms, we prove the stability using the induction method. Numerical experiments show the validity and the accuracy of the scheme, along with its efficiency.
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