Towards Analytic Solutions of infiltration Equations

Joash Gobin, Dwayne Renville and Michael Hackett

📃• URC22 Abstract • 

Published: May 18, 2022Book of Abstracts of the 4th Undergraduate Research Conference. University of Guyana, Office for Undergraduate Research.


Joash Gobin ✉️ Dwayne Renville, Michael Hackett 1 Department of Mathematics, Physics & Statistics. Faculty of Natural Sciences. University of Guyana-Turkeyen Campus. Greater Georgetown, Guyana. 


The study of infiltration within the field of hydrology rests heavily on Richards equation, which, since its introduction in 1931 for infiltration in unsaturated soil, has had many solutions under particular sets of parameter constraints. There has also been numerical solutions that were verified with experimental data. Like many other differential equations in various fields of study, there is a preference for numerical solutions. Notwithstanding their utility, the reliance on numerical techniques often obscures the requirement of mathematical rigor and proof of corresponding analytic solutions. This research seeks to explore existing analytic solutions, under various parameter constraints, for the Richards equation. The approach adopted in this study is that of review of literature and mathematical formulation. Equations will be investigated in a sequential order from many to just a few constraints. The researcher expects to present detailed analytic solutions.

 

Keywords: Hydrology, Infiltration equations, Analytic solutions, Richards equation

 

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The 4th Undergraduate Research Conference (URC22) was hosted by the University of Guyana’s Office for Undergraduate Research on May 18-20, 2022.