# Modeling and Simulation of Tsunami Impact: A Short Review of Recent Advances and Future Challenges

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## Abstract

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`Github`repository to allow developers and model users to update the table with additional models as they are published and help with model discoverability.

## 1. Introduction

## 2. State of the Field in Tsunami Forward Modeling

## 3. Mathematical Representations and Assumptions

#### 3.1. The 3D Navier–Stokes Equations

#### 3.2. Depth-Averaged Models

#### 3.2.1. Scaled Equations

#### 3.2.2. Depth Integration

**Remark**

**1.**

#### 3.2.3. Approximations

#### 3.2.4. Shallow Water

#### 3.2.5. Not So Shallow Equations

#### 3.3. Mathematical Conclusions

## 4. Numerical Solution and Computational Considerations

- Flow scale and régime. For example, are we modeling breaking waves in the vicinity of the shore or linear waves propagating in the ocean basin? Is turbulence an important factor?
- Complexity of the physics needed. Here the difference between using a wall boundary condition at the shore and doing true wetting and drying may be significant as does the representation of true turbulent flow.
- Performance on the computing architecture being considered.
- Overall size of the problem considered. Is one interested in a single simulation or a large ensemble in order to account for uncertainty?

## 5. Towards a Multi-Scale Framework from Source to Impact

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Some available tsunami models. Acronyms used in this table: $SW$ Shallow Water, B Boussinesq, $SGN$ Serre–Green–Naghdi, $N-S$ Navier–Stokes, $SPH$ Smoothed Particle Hydrodynamics, $LES$ Large Eddy Simulation, $WM$ Wall Modeled LES, $RANS$ Reynolds Averaged Navier–Stokes equations, $FSI$ Fluid–Structure Interaction, $MP$ Multi-Phase capabilities for erosion and sediment transport, and $SD$ for spatial discretization. The use of $2D(1/2)$ indicates that the model can run in multi-layer modality [95]. Storm surge and ocean dynamics models are omitted.

Model | Space Dim. | Equations | Turbul. | Wave Break. | FSI | MP | SD |
---|---|---|---|---|---|---|---|

GeoCLAW [56] | 1D/2D/2D$\frac{1}{2}$ | $SW$ | No | No | No | No | FV |

NUMA2D [125,126] | 1D/2D | $SW$ | No | No | No | No | SE/DG |

MOST [92] | 1D/2D | $SW$ | No | No | No | No | FD |

Cliffs [92,127] | 1D/2D | $SW$ | No | No | No | No | FD |

Tsunami-HySEA [128,129,130] | 1D/2D | $SW/B$ | No | Yes | No | No | FV |

Multilayer-HySEA [131,132] | 1D/2D(1/2) | $SW/B$ | No | Yes | No | Yes | FV |

TUNAMI [133,134] | 1D/2D | $SW$ | No | No | No | No | FD |

NAMI-DANCE [135] | 1D/2D | $SW$ | No | No | No | No | FD |

COMCOT [136] | 1D/2D | $SW$ | No | No | No | No | FD |

SELFE [96] | 1D/2D | $SW$ | No | No | No | No | FE |

TsunAWI [97] | 1D/2D | $SW$ | No | No | No | No | FE |

TsunaFlash [137] | 1D/2D | $SW$ | No | No | No | No | FE/DG |

VOLNA [94,138] | 1D/2D | $SW$ | No | No | No | No | FV |

Delft3D [139] | 1D/2D | $SW$ | No | No | No | Yes | FD |

Basilisk [140,141,142] | 2D/3D | $SGN$ | No | Yes | No | Yes | FV |

BOSZ [143] | 1D/2D | B | No | No | No | No | FV/FD |

Celeris [144] | 1D/2D | B | No | No | No | No | FV |

FUNWAVE [145,146] | 1D/2D | B | No | No | No | No | FV/FD |

pCOULWAVE [147,148] | 2D/3D | B | Yes | No | No | No | FV |

NEOWAVE [149] | 2D | B | No | No | No | No | FD |

GPUSPH [98] | 3D | $SPH$ | No | Yes | No | No | SPH |

SCHISM [111] | 1D/2D/3D | $N-S$ | $RANS$ | Yes | No | No | FE/FV |

COBRAS [108,109] | 2D/3D | $N-S$ | $RANS$ | Yes | No | No | FD |

TSUNAMI3D [110,150] | 2D/3D | $N-S$ | $RANS$ | Yes | No | No | FD |

waves2FOAM [17,18,112] | 2D (tsunami) | $N-S$ | $RANS$ | Yes | No | No | FV |

NHWAVE [151] | 2D/3D | $N-S$ | LES | Yes | Yes | Yes | FV/FD |

Alya [90,152] | 2D/3D | $N-S$ | $LES/WM/RANS$ | Yes | Yes | Yes | FE |

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**Figure 1.**Pieces of the T$\overline{\mathrm{o}}$hoku multi-billion dollar tsunami protection wall after a level-2 tsunami his the coasts of Japan in 2011. While each individual concrete section of the wall did not suffer significant damage, the erosion at the foundations of the wall happened so quickly that the concrete barrier simply fell (Picture taken from in [13].).

**Figure 2.**Map of the Ring of Fire, a long coastal stretch that is most likely impacted by large tsunamis. Some tsunami mitigation parks are being constructed in South Java, Indonesia (Image: Indonesia Ministry of Marine Affairs and Fisheries), Miyagi Prefecture, Japan (Image: the Morino Project), and Constitución, Chile (Image: Architect Magazine). Adapted from the work in [12].

**Figure 3.**The off-shore tsunami is, effectively, a two-dimensional long-wave (

**left**, Chilean tsunami, 2010). On-shore, however, it becomes turbulent and multi-phase—water, sand, dirt, and debris (

**right**, T$\overline{\mathrm{o}}$hoku tsunami, Japan, 2011).

**Left**: adapted from NOAA Tsunami Warning System.

**Right**: image credit: Reuter/Kyodo found at www.theatlantic.com/photo/2011/03/earthquake-in-japan/100022/.

**Figure 4.**Two examples of flexible vegetation in a three-dimensional flow at large Reynolds number.

**Left**: bent idealized 1D vegetation submerged in a channel flow (adapted from the work in [88]).

**Right**: two-way fluid–structure interaction model of 3D idealized trees in a dam break triggered flow (image courtesy of Abhishek Mukherjee).

**Figure 5.**Representation of a comprehensive off-to-on-shore flow framework. The 3D Navier–Stokes solver is forced at the boundaries by the shallow water model of the tsunami off-shore, which is forced by an earthquake simulator. In fact, the 2D shallow water solver can extend all the way into the shore depending on the needs of the solver and compatibility layer.

**Figure 6.**Gravity-centered, depth-averaged coordinate system for the shallow water equations. Here h is the depth of the water column; $\eta $ the difference between a defined datum, commonly a given sea-level, and the sea-surface; and b the bathymetry surface as measured from the same datum.

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Marras, S.; Mandli, K.T.
Modeling and Simulation of Tsunami Impact: A Short Review of Recent Advances and Future Challenges. *Geosciences* **2021**, *11*, 5.
https://doi.org/10.3390/geosciences11010005

**AMA Style**

Marras S, Mandli KT.
Modeling and Simulation of Tsunami Impact: A Short Review of Recent Advances and Future Challenges. *Geosciences*. 2021; 11(1):5.
https://doi.org/10.3390/geosciences11010005

**Chicago/Turabian Style**

Marras, Simone, and Kyle T. Mandli.
2021. "Modeling and Simulation of Tsunami Impact: A Short Review of Recent Advances and Future Challenges" *Geosciences* 11, no. 1: 5.
https://doi.org/10.3390/geosciences11010005