Analytical and numerical solutions to describe water table fluctuations due to canal seepage and time-varying recharge

Abstract

Hybrid finite analytic solution (HFAS), Galerkin's method based finite element solution (FES) and fully implicit finite difference solution (FIFDS) of one dimensional nonlinear Boussinesq equation and Analytical solution of Boussinesq equation linearized by Baumann's transformation (analytical solution I, AS I) as well as linearized by Werner's transformation (analytical solution II, AS II) were employed to obtain water table rise in a horizontal unconfined aquifer lying between two canals located at finite distance having different elevations and subjected to various patterns of recharge, i.e. zero recharge, constant recharge, as well as time varying recharge. Considering HFAS as benchmark solution, water table in mid region as obtained from FES followed by FIFDS was observed quite close to that obtained from HFAS and as per L2 and Tchebycheff norms computation, it was ranked at first and second place, respectively. Both AS I and AS II predicted higher water table at t = 5 days but at t = 10 days, AS I predicted lower and AS II predicted higher water table at all distances due to linearization effect. So, analytical solutions of linearized Boussinesq equation were rated lower than numerical solutions of nonlinear Boussinesq equation. HIGHLIGHTS Two analytical solutions of linearized Boussinesq equation and three numerical solutions i.e., fully implicit finite difference solution, finite element solution and hybrid finite analytic solutions (HFAS) of nonlinear Boussinesq equation, were developed.; L2 and Tchebycheff norms values showed that values from Numerical solutions are quite close to HFAS compared to approximate analytical solutions.;

Keywords

• analytical solutions
• canal seepage
• linearized and nonlinear boussinesq equation
• numerical solutions
• time-varying recharge
• unconfined aquifer