Numerical Solution of Boussinesq Equation

by Sita Ram Singh, Assoc. Prof. of Agr. Engrg.; Dept of Soil and Water Engrg., Punjab Agr. Univ., Ludhiana, India,
C. M. Jacob, Officer on Special Duty; State Planning Board, Trirandrum, India,

Serial Information: Journal of the Engineering Mechanics Division, 1976, Vol. 102, Issue 5, Pg. 807-824

Document Type: Journal Paper


The Boussinesq equation is a mathematical model of unconfined ground-water flow. Since the equation is nonlinear, finite difference methods offer a possible technique for solutions. In this study, an extrapolated Crank-Nicolson finite difference scheme for one-dimensional Boussinesq equation with source and sink terms is described to model the flow through a phreatic aquifer lying between two open channels. Generalized traveling wave solutions of the same equation are also obtained. A comparison of the extrapolated Crank-Nicolson solution with a traveling wave solution confirms the accuracy of the former. Details of the response of an unconfined aquifer subject to different rates of recharge and withdrawal are presented.

Subject Headings: Numerical methods | Boussinesq equations | Mathematical models | Groundwater flow | One-dimensional flow | Aquifers | Hydrologic models | Nonlinear analysis

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