Development of a Tsunami Inundation Analysis Model for Urban Areas Using a Porous Body Model
Abstract
:1. Introduction
1.1. Background
- (Model 1) the roughness map model, which uses Manning’s roughness coefficient “n” according to the land-use type [27] (hereafter, Landuse-n model),
1.2. Objectives
1.2.1. Development of NSWW Theory and Numerical Model Based on a Porous Body Model
1.2.2. Investigation of Characteristics of Tsunami Hazards Simulated by Numerical Models
2. Nonlinear Shallow Water Wave Equations Based on a Porous Body Model
2.1. Governing Equations
2.2. Kinematic and Dynamic Boundary Conditions
2.3. Integration of the Continuity Equation
2.4. Integration of the Momentum Equation
3. Establishing the Porosity and Surface Permeability for a Group of Buildings
3.1. Porosity of the Water Column
3.2. Horizontal Surface Permeability of the Water Column
4. Differences between Conventional Porous-Type Models and the Proposed Model
5. Numerical Simulations of Tsunami Inundation in Onagawa, Miyagi Prefecture, during the Great East Japan Earthquake
5.1. Background of the Target Domain
5.2. Initial Setup of the Tsunami Simulation
5.3. Results and Discussions
6. Conclusions and Recommendations
- The proposed PBM exhibited as good accuracy for the inundation heights around building near the coastline as with conventional three-dimensional simulation with high resolution.
- In the case where the inundation area is restricted by the topography with a steep slope behind the urban area and the flow depth is much greater than the building height, the differences in the modeled building effects and computational resolution do not significantly affect the maximum water level near the coastline. Therefore, two-dimensional simulations with a practical resolution demonstrate good accuracy while estimating the inundation height near the coastline, although we must examine the applicability of these models to regions where the locality can become stronger in future work.
- A model that includes porosity can yield an increase in the water level, which makes it easier for the tsunami to spread out over the land, thereby decreasing the flow velocity.
- A model that includes the surface permeability restricts the progress of the tsunami according to the distribution of the buildings and reproduces a flow field concentrated along the straight road.
- By properly incorporating the porosity and the surface permeability into the theory and the numerical model, the model can adequately reproduce high flow velocities due to the increase in the gradient of the water surface and the concentration of the flow during the inundation process within the urban area. In addition, the water level at the time will increase due to the flow and geometric effects. Therefore, a numerical model that does not consider geometric effects could underestimate the local hydrodynamic force.
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Model | Geometric Effect | Mechanical Effect | Rough indication of Computational Cost | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Space Volume (Porosity) | Flow Path Area (Surface Permeability) | Building Height Effect | Bottom Friction | Drag Force | ||||||||
Wall Friction | Wake | Array Effect | ||||||||||
High Resolution | 3-D NS | VOF | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | >>104 | ||
SPH | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | >>104 | |||||
2-D NSWW | ✓ | ✓ | ✓ | ✓ | ✓ | 103 | ||||||
Practical Resolution (2D) | Roughness-Type Model | With DEM | Constant-n | (✓) | 1 | |||||||
○ Landuse-n | ✓ | (✓) | (✓) | (✓) | 1 | |||||||
Equivalent-n | ✓ | ✓ | ✓ | (✓) | 1 | |||||||
With DSM | ○ Landuse-n/Topography | (✓) | (✓) | (✓) | ✓ | (✓) | (✓) | (✓) | 1 | |||
Equivalent-n/Topography | (✓) | (✓) | (✓) | ✓ | ✓ | ✓ | (✓) | 1 | ||||
Porous-Type Model with DSM | ○ Coastal-Forest | ✓ | (✓) | ✓ | ✓ | ✓ | ✓ | (✓) | 1 | |||
Flood | ○ FDM | ✓ | (✓) | (✓) | ✓ | ✓ | ✓ | (✓) | 1 | |||
FVM | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | (✓) | 1 | ||||
○ PBM (FDM) (This Study) | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | (✓) | 1 |
Field Survey | Roughness-Type Model | Porous-Type Model | ||||
---|---|---|---|---|---|---|
Landuse-n | Landuse-n/ Topography | Coastal-Forest | Flood | PBM | ||
Inundation Area (km2) | 1.64 | 1.68 | 1.56 | 1.59 | 1.48 | 1.55 |
Ratio with Landuse-n | 0.98 | 1.00 | 0.93 | 0.95 | 0.88 | 0.93 |
Mean Value of 100% of Maximum Velocity (m/s) | - | 3.18 | 2.78 | 2.64 | 2.43 | 3.02 |
Mean Value of Top 30% of Maximum Velocity (m/s) | - | 5.34 | 4.69 | 4.50 | 4.21 | 5.42 |
Mean Value of Top 10% of Maximum Velocity (m/s) | - | 6.71 | 6.00 | 5.80 | 5.50 | 7.78 |
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Yamashita, K.; Suppasri, A.; Oishi, Y.; Imamura, F. Development of a Tsunami Inundation Analysis Model for Urban Areas Using a Porous Body Model. Geosciences 2018, 8, 12. https://doi.org/10.3390/geosciences8010012
Yamashita K, Suppasri A, Oishi Y, Imamura F. Development of a Tsunami Inundation Analysis Model for Urban Areas Using a Porous Body Model. Geosciences. 2018; 8(1):12. https://doi.org/10.3390/geosciences8010012
Chicago/Turabian StyleYamashita, Kei, Anawat Suppasri, Yusuke Oishi, and Fumihiko Imamura. 2018. "Development of a Tsunami Inundation Analysis Model for Urban Areas Using a Porous Body Model" Geosciences 8, no. 1: 12. https://doi.org/10.3390/geosciences8010012