Solving the Boussinesq Equation Using Solutions of the Blasius Equation

Abstract

The response of a water table to a sudden drawdown is examined assuming that it can be described by the Boussinesq equation. An approximate analytical solution of this equation is given. This solution is based on significant improvements to previous equations obtained by Heaslet and Alksne [1961]. In comparison with an “exact” numerical solution the new approximate solution gives a maximum error of 0.02%. Such an analytical result is not only of theoretical interest but could be used as a standard reference, for instance, to validate other analytical or numerical schemes.