Tsunami

Overview

In this benchmark we model the propagation of the 2011 Tohoku tsunami by solving the shallow water equations. For the numerical solution of the PDE, we apply an ADER-DG method implemented in the ExaHyPE framework. The aim is to obtain the parameters describing the initial displacements from the data of two available buoys located near the Japanese coast.

Tsunami-Model

Authors

Run

docker run -it -p 4242:4242 linusseelinger/model-exahype-tsunami

Properties

Model

Description

forward

Tsunami model

forward

Mapping

Dimensions

Description

inputSizes

[2]

x and y coordinates of a proposed tsunami origin

outputSizes

[4]

Arrival time and maximum water height at two buoy points

Feature

Supported

Evaluate

True

Gradient

False

ApplyJacobian

False

ApplyHessian

False

Config

Type

Default

Description

level

int

0

between 0 and 2, the model level to run (see below for further details)

verbose

bool

false

switches text output on/off

vtk_output

bool

false

switches vtk output to the /output directory on/off

Mount directories

Mount directory

Purpose

/output

VTK output for visualization

Source code

Model sources here.

Description

The underlying PDE model can be written in first-order hyperbolic form as

\( \frac{\partial}{\partial t} \begin{pmatrix} h\\hu\\hv\\ b \end{pmatrix} + \nabla \cdot \begin{pmatrix} hu & hv\\ hu^2 & huv\\ huv & hv^2 \\ 0 & 0\\ \end{pmatrix}+ \begin{pmatrix} 0\\ hg \, \partial_x (b+h)\\ hg \, \partial_y (b+h)\\ 0\\ \end{pmatrix}= 0, \)

where

  • \(h\) denotes the height of the water column,

  • \((u,v)\) the horizontal flow velocity,

  • \(g\) gravity

  • \(b\) denotes the bathymetry.

This benchmark creates a sequence of three models:

  1. First model:

    • bathymetry is approximated only by a depth average over the entire domain

    • pure DG discretisation of order 2

  2. The second model:

    • DG discretisation with a finite volume subcell limiter allowing for wetting and drying

    • smoothed bathymetry data (Gaussian filter)

  3. The third model:

    • DG discretisation with a finite volume subcell limiter allowing for wetting and drying

    • full bathymetry data