Semianalytical Time Integration for Transient Groundwater Flow in Confined Aquifers

Abstract

A semianalytical time integration method is proposed for the ordinary differential equations produced by the spatial discretization of the transient groundwater flow equation. Instead of approximating the time derivative by finite difference, the proposed method approximates the exact solution of the ordinary differential equations. The method is unconditionally stable; the accuracy depends only on the approximation accuracy of the stress; for piecewise constant or linear stress (e.g., pumping) in time, the solution can be exact; and the time step size can be as long as a stress period. The tradeoff is the computational cost, which can be reduced by using larger and less variable time step sizes. Two examples are given to show the performance of the semianalytical time integration method.