International Workshop on Long-Wave Runup Models 2-Dimensional Model with Boundary-Fitting Cell System Benchmark #2:Tsunami Runup onto a Complex 3Dimensional Beach Hiroyasu YASUDA Civil 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

International Workshop on Long-Wave Runup Models How to Create the BFC Create procedure is very importance. # Step1: Assign Ridge & Valley line. # Step2: Cell-side must accord with Contour as much as possible.

International Workshop on Long-Wave Runup Models BFC for Monai pocket beach y x x=4.950, y=1.825 x=5.715, y= cm z=7.5cmz=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 cm 2 – Range ～ cm 2 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 = (s) Manning's n = Numerical Scheme : Explicit FDM, Leap-Flog

International Workshop on Long-Wave Runup Models Definition of Calculation Point Eq.: Expanded Linear Long wave theory. 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. BFC Area 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 = (s) Manning's n = 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 BFC Area Visualizing Area (2D Shallow water)

International Workshop on Long-Wave Runup Models Calculation Results - Monai area y x z=0.00cm z=2.50cm z=7.50cm x=3.000 y=1.000 x=5.488, y=2.902 BFC Area t =17.70 sec, Maximum runup at Monai. Maximum height: 7.10cm 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 Depth of Water (cm) Maximum Inundation area at (s).

International Workshop on Long-Wave Runup Models Calculation Results of BFC area by 2D Shallow water Eq Depth of Water (cm) Maximum Inundation area at (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 !

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