Simulating the Effects of Dam Breakage on the Downstream Topography: Morphological Evolution of Mounds and a Furrow
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Date
2015-12
Authors
Magua, Amos Ng'ang'a
Journal Title
Journal ISSN
Volume Title
Publisher
Kenyatta University
Abstract
In this work we apply a nite 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
ooding downstream of the breach location.
The considered mathematical model comprise of shallow water equations
coupled with the bed updating equation which is modi ed to account for
sediment entrainment process. Thus the model comprises a set of highly nonlinear
hyperbolic partial di erential equations written in compact conservation
form. In order to ensure that the resulting
ux matrices are non-singular and
are in compact conservation form, C-formulation was used. This formulation
is an unsteady approach where the water
ow 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 di erential equations
written in C formulation were rst 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 nally the
time discretization (full discretization) was done using implicit-explicit Runge
kutta scheme. The numerical model developed was used to simulate dam break
ows 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 signi cantly a ected topography containing the furrow. The
furrow widened and became shallower. Secondly the entrainment and the bed
load sediment transport signi cantly a ected 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.
Description
A thesis submitted in partial full lment for the Degree of
Doctor of Philosophy (Ph.D) in Applied Mathematics in
the School of Pure and Applied Sciences of
Kenyatta University, December 2015