Geoscience Reference
In-Depth Information
2D Simulation of Discontinuous Shallow Flows
R. Canelas, J. Murillo, and R. Ferreira
1
Introduction
Open channels with mobile boundaries are subjected to entrainment, erosion,
transport, and deposition of sediments. During intense floods, such as those origi-
nated by dam failure, bedload can be intense, leading to flow stratification: an
uppermost layer of clean water and a lowermost layer of sheetflow can be observed.
Such flows will herein be designated geomorphic flows. Since the physical system
comprises a stratified mixture of fluid and granular matter, conservation equations
must take into account such stratification along with the influence of sediment on
inertia and pressure terms in the momentum balance. In the case of a purely
IVP-Riemann problem, Ferreira (
2005
,
2008
) showed that the system of conserva-
tion equations describing geomorphic flows is structurally similar to the clean water
system. The main difference is that, considering equilibrium sediment transport, a
new Riemann wave is introduced, expressing a genuinely nonlinear characteristic
field, associated to the conservation of granular material in the transport layer. This
new discontinuity is weak and unsusceptible to bring about major errors in the
approximate Riemann solvers based on the clear-water conservation equations for
conservative finite-volume discretization. Considering nonequilibrium sediment
transport, the wave structure is identical to that of the clear-water problem as the
extra equation; the mass conservation of the bed is formally uncoupled.
The purpose of this work is to present a 2DH mathematical model suited for
potentially discontinuous geomorphic flows over complex geometries. The model
will be based on the clear-water conservation equations and will later be adapted
to mobile bed simulations.
