A new approach to capture heterogeneity in groundwater problem: An illustration with an Earth equation

¹ Institute for Groundwater Studies, Faculty of Natural and Agricultural Science, University of Free State, 9300 Bloemfontein, South Africa.
² Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia.

^* Corresponding author: AtanganaA@ufs.ac.za

Received: 20 September 2018
Accepted: 3 December 2018

Abstract

One of the major problem faced in modeling groundwater flow problems is perhaps how to capture heterogeneity of the geological formation within which the flow takes place. In this paper, we suggested applied a newly established approach to model real world problems that combines the concept of stochastic modeling in which parameters inputs are converted into distributions and the time differential operator is replaced by non-local differential operators. We illustrated this method with the Earth equation of groundwater recharge. For each case, we provided numerical and exact solution using the newly established numerical scheme and Laplace transform. We presented some numerical simulations. The numerical graphical representations let no doubt to think that this approach is the future way of modeling complex problems.