Numerical Analysis of Fluid Flow Due to a Dam Break: A Case of Solai Dam Break Nakuru County, Kenya
Momanyi Christopher
*
Department of Mathematics and Actuarial Science, Kenyatta University, Kenya.
*Author to whom correspondence should be addressed.
Abstract
In this paper we model a dam break flow using the FTCS (Forward Time Central Space) numerical scheme to estimate the inundation extents caused by failure of a dam: a case for Solai earthfill Dam in Nakuru County, Kenya. This numerical model is based on the Shallow Water Equations (SWEs) that are extensively applied in depicting shallow water flows behavior in hydraulic engineering. The dam’s downstream topography and measured height of the water initially are used as the parameters for this numerical simulation. The numerical simulation of the dam break that provided the inundation map were carried as follows: - spatial discretization carried out using the Central Difference Finite scheme, to cater for any discontinuities arising from the steep gradients; Hansen filters were applied at various nodes, and the time discretization carried out using the Forward Difference Finite numerical method. The two discretization methods mentioned herein add up to the Forward Time Central Space (FTCS) numerical scheme. The inundation map results are compared to the actual Solai Dam failure flooding extent and the performance, accuracy and computation complexity of the method (FTCS) compared to the Monotone Stream Upstream Centered Scheme for Conservation Laws (MUSCL) numerical scheme.
Keywords: Numerical analysis, fluid flow, shallow water equations