In this work we apply a finite volume discretization technique based on a relaxation scheme to simulate the morphological evolution of the topography as a result of a dam break, that causes flooding downstream of the breach location. The considered mathematical model comprise of shallow water equations coupled with the bed updating equation which is modified to account for sediment entrainment process. Thus the model comprises a set of highly nonlinear hyperbolic partial differential equations written in compact conservation form. In order to ensure that the resulting flux matrices are non-singular and are in compact conservation form, C-formulation was used. This formulation is an unsteady approach where the water flow and bed update are discretised simultaneously. The resulting Jacobian matrices could not be diagnolised easily and the eigenvalues were determined using the formulae for cubic functions as given by Spiegiel and Liu (1999). The non-linear partial differential equations written in C formulation were first relaxed into a set of linear hyperbolic system using the relaxation variables V~ = (V1, V2, V3, V4), W~ = (W1, W2, W3, W4). The relaxed equations were then discretized spatially (semi-discretization) using the Vanleer’s MUSCL scheme which is total variation diminishing, and finally the time discretization (full discretization) was done using implicit-explicit Runge kutta scheme. The numerical model developed was used to simulate dam break flows and sediment transport on topographical surfaces with a deep narrow furrow and a topographic surface with two mounds located downstream of the breach location. Results on simulations showed that the entrainment and bed load transport significantly affected topography containing the furrow. The furrow widened and became shallower. Secondly the entrainment and the bed load sediment transport significantly affected the topography containing the two mounds. The mounds were eroded and there was high depositions of the sediments in the vicinity of the mounds and thirdly the dam break scenario with entrainment had a higher morphological evolution than the dam break scenario without the entrainment. The results thus obtained showed that the model is conservative, accurate, stable, robust, capable of resolving shocks and can handle even more complex geometries including simulations of real life dam break scenarios.
Ng’ang’a, M (2021). Simulating The Effects Of Dam Breakage On The Downstream Topography: Morphological Evolution Of Mounds And A Furrow. Afribary. Retrieved from https://afribary.com/works/simulating-the-effects-of-dam-breakage-on-the-downstream-topography-morphological-evolution-of-mounds-and-a-furrow
Ng’ang’a, Magua "Simulating The Effects Of Dam Breakage On The Downstream Topography: Morphological Evolution Of Mounds And A Furrow" Afribary. Afribary, 28 May. 2021, https://afribary.com/works/simulating-the-effects-of-dam-breakage-on-the-downstream-topography-morphological-evolution-of-mounds-and-a-furrow. Accessed 24 Sep. 2023.
Ng’ang’a, Magua . "Simulating The Effects Of Dam Breakage On The Downstream Topography: Morphological Evolution Of Mounds And A Furrow". Afribary, Afribary, 28 May. 2021. Web. 24 Sep. 2023. < https://afribary.com/works/simulating-the-effects-of-dam-breakage-on-the-downstream-topography-morphological-evolution-of-mounds-and-a-furrow >.
Ng’ang’a, Magua . "Simulating The Effects Of Dam Breakage On The Downstream Topography: Morphological Evolution Of Mounds And A Furrow" Afribary (2021). Accessed September 24, 2023. https://afribary.com/works/simulating-the-effects-of-dam-breakage-on-the-downstream-topography-morphological-evolution-of-mounds-and-a-furrow