PARMA UNIVERSITY SIMULATIONS OF THE ISOLATED BUILDING TEST CASE F. AURELI, A. MARANZONI & P. MIGNOSA DICATeA, Parma University Parco Area delle Scienze.

PARMA UNIVERSITY SIMULATIONS PARMA UNIVERSITY SIMULATIONS

OF THE OF THE

ISOLATED BUILDING TEST CASEISOLATED BUILDING TEST CASE

F. AURELI, A. MARANZONI F. AURELI, A. MARANZONI && P. MIGNOSA P. MIGNOSA

DICATeA, Parma UniversityDICATeA, Parma University

Parco Area delle Scienze 181/A – 43100 Parma, ItalyParco Area delle Scienze 181/A – 43100 Parma, Italy

33rd rd IMPACT WorkshopIMPACT WorkshopUCL, Louvain-la-Neuve, BelgiumUCL, Louvain-la-Neuve, Belgium

November 6 - 7, 2003November 6 - 7, 2003

1. Recall of governing equations and description of numerical models

2. Comparison between experimental data and numerical results for the Isolate Building Test Case

Validation of the capabilities of 2D FVM numerical codes in modelling rapidly varying flows induced by dam or levee breaks in which the presence of obstacles induces near field effects in the flow field

Aim of the study:

INTRODUCTIONINTRODUCTION

Summary of the presentation:

33rd rd IMPACT Workshop - November 6 - 7, 2003 UCL, Louvain-la-Neuve, BeIMPACT Workshop - November 6 - 7, 2003 UCL, Louvain-la-Neuve, Be

with:

310

310 2

0

222

20

222

,hC

vhuhvhnS

hC

vhuhuhnS fyfx


2D SHALLOW WATER 2D SHALLOW WATER EQUATIONSEQUATIONS

AA C

dAdCdAdt

dSnHU with: )( GF,H tensor of fluxes

Unsplit finite volume discretization of homogeneous advection problem

n

j,i

n

yxt

U)t,y,x(U

)U(G)U(FU 0

Solution:

ttadvj,iU

)gg(y

t)ff(

x

tUU n

/j,in

/j,in

j,/in

j,/inj,i

advj,i 21212121

where

n/j,i

n/j,i

nj,/i

nj,/i g,g,f,f 21212121 are numerical fluxes

jj yy

xx

ii

n

j,/if 21n

j,/if 21

n

/j,ig 21

n

/j,ig 21


FINITE VOLUMESFINITE VOLUMESNUMERICAL MODELSNUMERICAL MODELS


SLICSLICNUMERICAL MODEL (I)NUMERICAL MODEL (I)

•Second order accurate in space due to linear extrapolation of variables (MUSCL technique)

•Second order accurate in time due to t/2 evolution of extrapolated variables

ni,j

n,ji,ji

n,ji

ni,j,ji

ni,j

L,ji kk UUΦUUΦUU

12/112/12/1 1

4

11

4

1

ni,j

n,ji,ji

n,ji

ni,j,ji

ni,j

R,ji kk UUΦUUΦUU

12/112/12/1 1

4

11

4

1maximum upwinding if k = -1

Ri,j

Li,j

i,j

R,ji

L,ji

i,j

Lji

L,ji

y

t

x

t2/12/12/12/1,2/12/1

22

UGUGUFUFUU

Ri,j

Li,j

i,j

R,ji

L,ji

i,j

Rji

R,ji

y

t

x

t2/12/12/12/1,2/12/1

22

UGUGUFUFUU


SLICSLICNUMERICAL MODEL (II)NUMERICAL MODEL (II)

•TVD Property satisfied by the application of Van Leer “limiter” function

•Numerical fluxes evaluated by an hybrid centred technique that applies Lax-Friedrichs and Richtmyer methods in two steps (FORCE scheme – Toro, 1997).

•Explicit, stability satisfied for the application of Courant-Friedrichs-Lewy condition

),(2

1),(

2

1),( 2/12/1,2/12/12/1,2/12/12/1,2/1,2/1

L,ji

R,ji

LFji

L,ji

R,ji

RIji

L,ji

R,jiji

FORCEji UUfUUfUUff


WAFWAFNUMERICAL MODEL (I)NUMERICAL MODEL (I)

•Second order of accuracy can be achieved by solving the conventional piecewise constant Riemann problem and using the solution averaged over space and time•The averaging takes the form of an integral of the flux over some volume

,,

where0

2212

hu

ghhu

uh

h

uh

h

xt

FU

FU

dtdxtxxxtt

t

t

x

x

WAFi

,

11 *

1212

2

1

2

121 Uff

•The scheme can be extended to two space dimensions via space operator splitting (Strang splitting)

dxtxx i

x

x

WAFi

2,1

21

21

212

1 Uff)(

1

121

21

ki

N

kk

WAFi w

ff

1,1, 10121 Nkkk ccccwN = 3 number of conservation laws,

weights expressed as a function of Courant number and wave Speed

x - split augmented homogeneous SWE


WAFWAFNUMERICAL MODEL (II)NUMERICAL MODEL (II)

•The conventional piecewise constant Riemann problem is solved using an approximate Riemann solver (HLLC)

•TVD Property satisfied by the application of well known “limiter” functions

•Explicit, stability satisfied for the application of Courant-Friedrichs-Lewy condition

m = 1, 2 vector component

•The exact solution of the Riemann problem in terms of the advected velocity v is:

s* = velocity in the star region

•The third component of the flux is:

ii

mi

miii

mii

miim

i SS

SSSS

1

)()(11

)(1

)(1)(

21

UUFFf

0* if

0* if

1 sv

svv

i

i

0* if

0* if

1)1(

)1(

)3(

21

21

21 sv

sv

ii

ii

i f

ff

Source term treatment with semi-implicit splitting technique

By second-order, implicit, trapezoidal method:

SOURCE TERM SOURCE TERM TREATMENTTREATMENT

adv

j,i

n

fo

U)t,y,x(U

)U(S)U(S)U(Sdt

dUtt

1nj,iU

)U(S)U(Qt

ItUU

)U(S)U(St

UU

)U(StUU

)U(S)U(St

UU

*

j,if

*

j,if

*

j,i

n

j,i

n

j,if

*

j,if

*

j,i

n

j,i

adv

j,io

adv

j,i

*

j,i

*

j,io

adv

j,io

adv

j,i

*

j,i

1

1

11

2

2

2


RESULTS (I)RESULTS (I)


Comparison between numerical and experimental water depths

0 5 1 0 1 5 2 0 2 5 3 0t (s )

0

0 .0 2

0 .0 4

0 .0 6

0 .0 8

0 .1

0 .1 2

0 .1 4

h (m

)

E x p erim en ta l d a ta

S L IC n u m erica l co d e

W A F n u m erica l co d e

G 1

0 5 1 0 1 5 2 0 2 5 3 0t (s )

0

0 .0 2

0 .0 4

0 .0 6

0 .0 8

0 .1

0 .1 2

h (m

)



E x p erim en ta l d a ta

S L IC o n C arte sian g rid

G 2

0 2 4

-1

1

0.00

0.03

0.06

0.09

0.12

0.15

0.18

0.21

0.24

mm

t = 2 0 s

waf

RESULTS (II)RESULTS (II)



0 5 1 0 1 5 2 0 2 5 3 0t (s )

0

0 .0 2

0 .0 4

0 .0 6

0 .0 8

0 .1

0 .1 2

0 .1 4

h (m

)



E x p e rim en ta l d a ta

G 3

0 5 1 0 1 5 2 0 2 5 3 0t (s )

0

0 .0 2

0 .0 4

0 .0 6

0 .0 8

0 .1

0 .1 2

0 .1 4

h (m

)




G 4

RESULTS (III)RESULTS (III)



0 5 1 0 1 5 2 0 2 5 3 0t (s )

0

0 .0 2

0 .0 4

0 .0 6

0 .0 8

0 .1

0 .1 2

h (m

)




G 5

0 5 1 0 1 5 2 0 2 5 3 0t (s )

0

0 .0 5

0 .1

0 .1 5

0 .2

0 .2 5

0 .3

0 .3 5

0 .4

0 .4 5

h (m

)




G 6

RESULTS(IV)RESULTS(IV)


Comparison between numerical and experimental velocities

t = 1 sec

WAF code on Cartesian domain

0 1 2 3 4 5 6x (m )

-1

0

1

y (m

)

0 .0

0 .5

0 .7

0 .9

1 .1

1 .3

1 .5

1 .7

1 .9

2 .1

2 .3

2 .5

RESULTS(V)RESULTS(V)



t = 5 sec


0 1 2 3 4 5 6x (m )

-1

0

1

y (m

)

0 .0

0 .5

0 .7

0 .9

1 .1

1 .3

1 .5

1 .7

1 .9

2 .1

2 .3

2 .5

RESULTS(VI)RESULTS(VI)



t = 10 sec


0 1 2 3 4 5 6x (m )

-1

0

1

y (m

)

0 .0

0 .5

0 .7

0 .9

1 .1

1 .3

1 .5

1 .7

1 .9

2 .1

2 .3

2 .5

CONCLUSIONSCONCLUSIONS


The numerical water level histories fit satisfactorily the experimental ones apart from Gauge n° 2.

This is probably due to nearness of the Gauge to the Hydraulic jump induced by the building. The spatial location of the hydraulic jump is not matched well. At a short distance from Gauge n° 2 the jump is present and the water depths are in better agreement with experimental ones.

Moreover in one of the models the description of the building in the Cartesian domain is approximate being the building sides not parallel to the co-ordinate axes.

Computed velocities are caught fairly well by the numerical models.

Despite not-negligible differences at a local scale, it seems that the proposed 2D models are capable to reproduce in a satisfactory way the overall characteristics of the phenomenon under study.

ACKNOWLEDGMENTSACKNOWLEDGMENTS


The Authors wish to acknowledge the European Commission, the IMPACT project team, Dr. Eng. S. Soares Frazão and Prof. Yves Zech for providing the experimental data concerning the isolated building test case.

PARMA UNIVERSITY SIMULATIONS OF THE ISOLATED BUILDING TEST CASE F. AURELI, A. MARANZONI & P. MIGNOSA DICATeA, Parma University Parco Area delle Scienze.

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