CUDAMCUDAM

Department of Civil and Environmental EngineeringDepartment of Civil and Environmental Engineering

University of TrentoUniversity of Trento

Zaragoza, Nov 3th-5th 2004IMPACT Investigation of Extreme Flood Processes & Uncertainty

Composition of the numerical group:L. Fraccarollo M. GiulianiG. Rosatti

=> The simulation starts at the dyke

=> Fulling coupling hydro-morphodynamics

=> We represent the real section and interpolate in between

=> Finite-volume conservative scheme (Fraccarollo et. al. 2003)

1D mathematical and numerical approach

1D mathematical model

2

12

)1()1(

))(1()1(

0)()()(

0)(

gIcR

A

x

zgAc

gIAucx

uAct

cuAx

zct

bcAt

uAx

zt

bAt

wh

b

c

bbs

bs

y

z

A wet area, u average velocity, bs width at surface, zb average bottom-elevation, c average concentration, cb bottom oncentration, wwater density, s sediment density, I1 first order of the wetted cross

section with respect to the free surface; I2 spatial derivative of the

first moment I1, Rh hydraulic radius, bottom shear-stress, c Coriolis compensation coefficient.

Starting assumptions for the 1D modelling

There is no account for the bedrock profile (future work)

drainagelake

lakedrainage Qdt

dAQ

dt

dV

)( lakelake functA

)(tlake

32

2

gb

Qh

hz

dykecrit

critlakedykeb

)(tz dykeb

Data section input BED and ROCK

Results

-10

40

90

140

190

240

290

340

0 5 10 15 20 25 30 35

distance [km]

ele

va

tio

n [

m s

.m.m

.]

thalweg init (t = 0 h)

thalweg fin (t = 120 h)

thalweg Q_l max (t = 40 h)

Results

Rock

outcrop

Results

-10

40

90

140

190

240

290

340

0 5 10 15 20 25 30 35

distance [km]

ele

vati

on

[m

s.m

.m.]

Rock

thalweg init

thalweg fin

1

4

3

2Rock out

Section

Strano che non affiori la roccia

Results section

80

90

100

110

120

130

140

150

160

170

0 50 100 150 200 250 300 350

coord y [m]

ele

va

tio

n [

m s

.m.m

.]

t = 0 h

t = 40 h

t = 120 h

rock

SECTION 1

50

70

90

110

130

150

170

190

210

230

250

0 100 200 300 400 500 600

coord y [m]

ele

va

tio

n [

m s

.m.m

.]

t = 0 h

t = 40 h

t = 120 h

rock

SECTION 2

200

205

210

215

220

225

230

235

240

0 50 100 150 200

coord y [m]

ele

va

tio

n [

m s

.m.m

.]

-100

-50

0

50

100

150

200

t = 0 h

t= 40 h

t = 120 h

rock

SECTION 3

300

310

320

330

340

350

360

0 50 100 150 200 250 300

coord y [m]

ele

va

tio

n [

m s

.m.m

.]

t = 0 h

t = 40 h

t = 120 h

rock

SECTION 4

Results

Rock outcrop Trento

Volume

-250000

-200000

-150000

-100000

-50000

0

50000

0 5000 10000 15000 20000 25000 30000 35000

distance [m]

volu

me

cum

ulat

o [m

3 ]

upstream

downstream

-40000

-30000

-20000

-10000

0

10000

20000

30000

0 5000 10000 15000 20000 25000 30000 35000

distance [m]

volu

me

[m

3 ]

upstream

downstream

=> The simulation includes the upstream lake

=> Fulling coupling hydro-morphodynamics (following 1D)

=> Rectangular computational cells

=> Finite volume extension of the 1D conservative scheme

2D mathematical and numerical approach

Two-phase mixture:

water sediments

(u,v) (up,vp)

Definition of the angle-phase displacements :

Grain trajectory

Mathematical model with the angle-phase displacements

Mass balance:

solid

liquid+solid

Momentum balance:

liquid+solid y - direction

liquid+solid x - direction

Some details on Ha!Ha! simulations

=> The breach has not been represented

=> The qinput is inserted far-away from the dyke, with no momentum

=> Initial conditions: downstream of the dyke there is no water

=> No informations about sediments

Hints to preliminary results

Problems:

=> Sediment fluxes have to corrected in our Riemann approximate solver

=> Boundary are saw-edged represented

=> Bank erosions and angle-phase displacements have to be included yet