International Workshop on Long-Wave Runup Models

2-Dimensional Modelwith Boundary-Fitting Cell SystemBenchmark #2:Tsunami Runup onto a Complex 3Dimensional Beach

Hiroyasu YASUDACivil Engineering Research Institute, I.A.I, Japan

International Workshop on Long-Wave Runup Models

Approach

Major cause of extreme run-up height, 32m are occurred by the effect of topography rather than the 3D effect ?

When fine grids properly represent the topography in 2D model, we can obtain accurate calculation results ?

In this study, focus on the Representation of Topography.

International Workshop on Long-Wave Runup Models

Concept of the BFC System

Cartesian coordinates, which are rectangle gird can’t freely represent characteristics of the topography using realistic grid size.

Triangle can freely represent all shape.

Boundary-Fitting Cell (B.F.C.) represent characteristics of the topography using Triangle cell.

– BFC was developed for numerical analysis of flood-Inundation flows on complex urban area with Drainage network and Wall in (Yasuda et al, 2001).

# 2D models with BFC was applied to Monai where is complex 3 Dimensional Beach.

International Workshop on Long-Wave Runup Models

BFC Area

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BFC Area

International Workshop on Long-Wave Runup Models

How to Create the BFC

Create procedure isvery importance.

# Step1: Assign Ridge & Valley line.# Step2: Cell-side must accord withContour as much as possible.

International Workshop on Long-Wave Runup Models

BFC for Monai pocket beach

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y

xx=4.950,y=1.825

x=5.715, y=2.050 2.5cm

z=7.5cm z=10.0cm

z=5.0cm

International Workshop on Long-Wave Runup Models

BFC of Monai pocket beach

Number of Cells: 670

Area of Cell:– Average 0.625 cm2

– Range 0.125～ 2.185 cm2

Side-length of Cell:– Average 1.25 cm– Range 0.5～ 3.25 cm

Cell size is approximately half of 1.4 cm rectangle gird.

International Workshop on Long-Wave Runup Models

Equations & I.C., B.C.

Eq.: Expanded Linear Long wave theory for BFC.

B.C.: Temporal water-level variations on boundary cells.

I.C.: D = 0.0 at the whole area M.B.C.: Tohoku Univ. model dt = 0.00125(s) Manning's n = 0.025 Numerical Scheme : Explicit FDM, Leap-Flog

International Workshop on Long-Wave Runup Models

Definition of Calculation Point

Eq.: Expanded Linear Long wave theory.

Qi

ë

Qi

Qi

l

aiai+1

Që

ë

Continuity Equation

Momentum Equation

International Workshop on Long-Wave Runup Models

Cell for Boundary

On boundary cells,Temporal water-level variations, which were calculated by shallow water theory are given.

International Workshop on Long-Wave Runup Models

BFC & Rectangle Grid area

B.C. & I.C.

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Reflective

Reflective

2D Shallow Water Area

International Workshop on Long-Wave Runup Models

Equations & I.C., B.C.

Eq.:2-D nonlinear long wave theory

B.C.– North & South wall : Reflective– East wall : Runup & Reflective– West wall : Incident wave

I.C.: x,y direction Flux = 0.

International Workshop on Long-Wave Runup Models

C.C. & Numerical Scheme

dx = dy =0.014 (m) dt = 0.00125 (s) Manning's n = 0.025 at the whole area Numerical Scheme

– Local and Pressure term : Leap-Frog (2nd order)– Convection term : Up-wind (1st order)– Friction term : semi implicit

C.F.L = 0.12

International Workshop on Long-Wave Runup Models

Visualizing Area

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Visualizing Area(2D Shallow water)

International Workshop on Long-Wave Runup Models

Calculation Results - Monai area

y

xz=0.00cm

z=2.50cm

z=7.50cm

x=3.000y=1.000

x=5.488, y=2.902

BFC Area

t =17.70 sec, Maximum runup at Monai.

Maximum height:7.10cm

2.251.500.750.00-0.75-1.5-2.25

Water Level (cm)

International Workshop on Long-Wave Runup Models

Calculation Results - Temporal water-surface variations

Ch.7 (x = 4.521, y = 1.696)

Ch.5 (x = 4.521, y = 1.196)

Ch.9 (x = 4.521, y = 2.196)

International Workshop on Long-Wave Runup Models

Calculation Results of BFC area

3.02.52.01.51.00.50.0

Depth of Water (cm)

Maximum Inundation areaat 17.90 (s).

International Workshop on Long-Wave Runup Models

Calculation Results of BFC area by 2D Shallow water Eq.

3.02.52.01.51.00.50.0

Depth of Water (cm)

Maximum Inundation areaat 17.70 (s).

International Workshop on Long-Wave Runup Models

Conclusions

If we can use the fine grid as about 5 m,2D model with Tohoku Univ. M.B.C is sufficient in order to reproduce the runup-height on complex 3D beach.

The BFC system can freely represent the topography, and has various possibilities !

International Workshop on Long-Wave Runup Models

Animation gallery

If you want to watch the animation files, Please visit web site of our lab.

URL: http://river.ceri.go.jp/data/yasu/catalina/index.html