1. Instituto Superior Técnico instituto superior técnico
Lake Ha!Ha! Case Study
mathematical model and results
Instituto Superior Técnico
Rui Ferreira
João Leal
A. H. Cardoso
A. B. Almeida
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Introduction
Structure of the presentation:
geometry for 1D computations
model presentation
initial and boundary conditions
flood propagation over mobile bed
conclusions and discussion
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Geomertry
raw data (362 sections with a 10 m discretization) is converted into trapezoidal sections
elevation and width of the thalweg and inverse bank slope are retained m 1 Bf
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Geomertry
slope is corrected in order to eliminate counter-inclined reaches
thalweg width and bank slope are subjected to a moving average and splining smoothening process
a linear interpolation process generates sections every Dx = 10 m
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Geomertry
River Ha!Ha! is divided in seven reaches (roughly at bedrock emergence points)
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Mathematical Model
conservation equations
closure equations
water mass
total momentum
sediment mass
transport layer
bed load concentration
total concentration
bed shear stress
characterisitc diameter of the sediment: ds = 0.01 m
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Mathematical Model
numerical discretization:
flux vector splitting scheme with Roe approximations (first order version only) for the equations of conservation of the water constituent
box scheme for the equation of conservation of sediment
uncoupled model with water depth correction at the end of each time step
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8. Initial & Boundary Conditions
upstream:
combined hydrograph at the upstream section of reach A
sediment hydrograph in every generic reach
downstream:
transmissive boundary condition downstream for the water depth
outflow hydrograph of each reach is used as upstream hydrograph for the following reach
note:
method of characteristics is used on both boundaries to determine the remaining hydrodynamic variables
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9. Initial & Boundary Conditions
initial condition is a steady flow over fixed bed and Q = 35 m3/s
fixed bed flow evolves from finite depth (0.5 m typically), zero discharge initial flow after a warm-up run
note that subcritical and supercritical flow coexist separated by hydraulic jumps
Ks = 75 m1/3s-1
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Flood Propagation
water depths
variation of bed elevation
note that subcritical flow disapears when mobile flow simulation starts
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Flood Propagation
longitudinal profiles during the maximum discharge
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12. Conclusions & Discussion
difficulties encountered
steady flow difficult to attain
downstream boundary condition is a source of non-physical waves
large simulation time
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