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collisional nature; and C is the bed, where horizontal movement of the sediments is
not important.
Ferreira (
2005
,
2008
) showed that the system of conservation equations
describing geomorphic flows is structurally similar to the clean water system,
where a new wave is introduced expressing the conservation of granular material
in layer B. In this work, emphasis will be placed on showing applications of the
model developed by Murillo and Garc
´
a-Navarro (
2010
). Hence, the conservation
equations to be solved will be the clear-water shallow-water equations, i.e., no
stratification or bedload will be considered and the influence of sediment density
in the inertia and pressure terms will be disregarded. Additionally, boundary
friction will be neglected as it is irrelevant to discuss the structure of the solutions.
The total mass and momentum conservation equations in the
x
and
y
directions
are thus:
@
t
h
þ @
x
ð
uh
Þþ@
y
ð
vh
Þ¼
0
(1)
g
h
2
2
Þþ@
x
u
2
h
@
t
ð
uh
þ
þ @
y
uvh
ðÞ¼
0
(2)
g
h
2
2
ðÞþ@
y
v
2
h
@
t
ð
vh
Þþ@
x
uvh
þ
¼
0
(3)
where
h
is the water depth and
u
and
v
are the flow velocities in
x
and
y
directions,
respectively.
3 Domain Discretization: Meshing
3.1 Generation and Refinement
The numerical solution of the partial differential equations (
1
-
3
) requires the
discretization of the computational domain in order to be able to replace the
continuous differential equations with a system of simultaneous algebraic differ-
ence equations. In the finite-volume methods, the discretization is accomplished by
dividing the computational domain into cells. The choice between a structured and
an unstructured mesh nature follows from the nature of the work at hand; since the
model must be prepared to deal with realistic, thus highly irregular domains, the
unstructured type of mesh is chosen for this work.
The mesh generator employed was Gmsh, chosen for its built-in pre- and
postprocessing capabilities. This generator provides three algorithms to generate
unstructured surface meshes. The Frontal algorithm is preferred for the high quality
of the output mesh.
This work uses conditions from two separate domains in order to locally control
the mesh density, the spatial gradients from the hydrodynamic variables and from
