Finite Difference Solution of Boussinesq Unsteady‐State Equation for Highly Sloping Lands

Abstract

Various analytical and numerical solutions are available for the steady‐state form of Boussinesq's equation describing the phreatic surface on sloping lands. Except for the experimental results of Luthin and Guitjens (1967), however, no analytical or numerical solution is available for the unsteady‐state drainage of highly sloping lands. A finite difference solution has been obtained for the nonlinear unsteady‐state differential Boussinesq equation for drainage of sloping lands. The unsteady‐state solutions for higher slopes of up to 70% are presented and compared with the Luthin and Guitjens solutions. The proposed solution compares reasonably well with experimental solutions for up to 30% slope, but beyond that, the solutions tend to deviate substantially.