There are several numerical codes in active development and available for use in tsunami simula- tion. Some of these are summarised below.
3DD
3DD is a three-dimensional hydrodynamic model used primarily in simulation of inter-tidal zones such as estuaries. Its robust wetting and drying scheme provides advantages for simulation of inun- dation over large areas of flat land. The scheme calculates water depth at each cell wall rather than
4.1. Background to numerical modelling 81
at the centre of the cell, as used by most other models. As one or more wall may be wet or dry at any time) it smooths the transition between cells, reducing the chance of spikes in velocity values of shallow flow. An effective depth term is also used to prevent instabilities caused by bed fric- tion. Other characteristics of the model are similar to other models: fully explicit time stepping, two-dimensional form based on momentum equation and conservation of mass (Prasetya et al., 2011b), explicit finite difference (Eularian) scheme, roughness length and eddy viscosity included, nonlinear convection acceleration and coriolis terms, free/no slip of land-sea boundaries, staggered grid, fully explicit leapfrog scheme. The fully explicit timestepping feature minimises numerical dispersion, however, this feature requires very small timesteps, which increases the computation- al expense of running this model. The model has been validated for tsunami using benchmark problems (Borrero et al., 2007) and other ‘skill score’ tests. 3DD allows the implementation of Boussinesq terms to simulate depth-dependent breaking and consequent energy loss. This model has been used by Prasetya et al. (2011b) to reproduce inundation and flow speeds in the 2004 Indi- an Ocean tsunami, in which they highlighted the importance of flow speeds in determining damage distribution and disparities in timing and spatial characteristics of return flow compared to onshore flow. Particularly, return flow was initiated before maximum inundation of prior wave is reached, is more concentrated than onshore flow and continues 500 m offshore (Prasetya et al., 2011b).
Australian National University-Geoscience Australia (ANUGA)
ANUGA1is an open source code developed to simulate tsunami as part of the Australian Tsunami Warning System. The conservative form of SWE are applied in a two-dimensional finite-volume method on a triangular mesh, with a focus on modelling inundation, therefore the model includes a wetting-drying function and ability to model hydraulic jumps (Geoscience Australia and the Aus- tralian National University, 2010; Jakeman et al., 2010), which makes it particularly suitable for modelling shallow flows around structures, such as in an urban environment. Frictional resistance is applied using Manning’s formula. As with other two-dimensional models, ANUGA is limit- ed from representing breaking waves or three-dimensional turbulence. Spherical coordinates are not supported, therefore large-scale analyses (larger than 6°) cannot be conducted, limiting use of the model to local and regional studies. Importantly, ANUGA does not allow explicit source modelling so the initial source must be modelled in another piece of software, and the results of propagation used as a boundary condition for ANUGA (Jakeman et al., 2010). ANUGA has been validated against physical modelling of the 1993 Okushiri Island tsunami and applied in simula- tion of the 2004 Indian Ocean tsunami (Jakeman et al., 2010). At present, ANUGA requires further refinement in order to satisfy conservation of physical energy, even in smooth, frictionless flows (Mungkasi and Roberts, 2013).
82 4. Local tsunami inundation in Napier (Paper 1)
COrnell Multi-grid COupled Tsunami (COMCOT)
COMCOT enables linear and non-linear modelling of the conservative form of the SWE, in both Spherical and Cartesian coordinates. The conservative form solves for volume flux rather than velocity alone, therefore the equations retain validity in the nearshore area, where shallow water assumptions begin to break down due to the decreasing ratio of water depth to tsunami wavelength. The conservative form also provides better performance at local scales where bathymetric variation is significant (Wang and Power, 2011). An explicit leap-frog finite difference method is adopted to solve both linear and non-linear shallow water equations (Cho, 1995). Initial conditions comprise instantaneous and transient sea floor disturbance, landslides and initial water surface displacement. COMCOT has been validated against analytical and experimental benchmark problems (Liu, Yeh, and Synolakis, 2008; Liu et al., 1995b; Wang and Liu, 2008) and has proven accurate in re-producing field observations of past events (Gica et al., 2007; Liu, Cho, and Fujima, 1994; Liu et al., 1995b; Wang and Liu, 2006). In recent years, COMCOT has been used extensively by GNS Science for tsunami modelling in New Zealand. These studies include inundation modelling of distant-source and local-source tsunami at Gisborne (Wang et al., 2009), and tsunami hazard from the Southern New Hebrides and Kermadec subduction margins (Power and Gale, 2011). The methods applied in these studies provide a guide for the set-up of a suitable model for use in this study, and indeed, some of the data used in this study was originally developed for these earlier studies.
Method of Splitting Tsunami (MOST)
MOST was developed by the United States (US) National Oceanic and Atmospheric Administra- tion (NOAA) for tsunami modelling and real-time forecasting. It solves the nonlinear SWE in two directions, along-shore and onshore, separately rather than solving in two-directions. This in- volves splitting the governing equations into two sets — each with one spatial dimensionxandy with a finite-difference method. The model has been validated against standard benchmarks prob- lems (Liu, Yeh, and Synolakis, 2008). MOST is now used internationally for tsunami inundation forecast modelling, including the NOAA operational tsunami forecasting system. MOST has pre- viously been used to simulate at-shore tsunami wave heights for various scenarios on the Hikurangi subduction zone interface (Power, Reyners, and Wallace, 2008).
River and Coastal Ocean Model (RiCOM)
RiCOM solves non-linear SWE with terms to describe non-hydrostatic forces on a mesh of trian- gular of quadrilateral elements (Downes et al., 2005; Lane et al., 2011, 2013; Walters, Barnes, and Goff, 2006). Finite-volume method is used to calculate fluxes through the face of each element. This permits natural simulation of wetting and drying in intertidal and onshore areas. Free surface