Validating a tsunami model for coastal inundation

How do we trust that a given fluid model is suitable for simulating water waves as they approach and wash over the land? This talk presents some of the benchmark tests used to validate a tsunami model. Using our Julia implementation of a fluid model, we check how well it conserves mass, matches analytical solutions, and reproduces laboratory experiments.

A computational model of a physical process requires careful validation before it can be trusted to tell something useful about the world. In this research, we did not set out to formulate a new model, but to implement an existing formulation in Julia. The tsunami model presented by Yamazaki et al. in [1] is a depth-averaged, nonhydrostatic fluid model with a free surface, capable of simulating tsunami waves as they transform and run up on land. Though the authors presented their validation results, we still needed a suite of tests to help verify that our implementation matches the specification, and that it is suitable for our application area.

In this talk, we will explore the following kinds of validation tests for numerical tsunami models by walking through examples with our Julia implementation.

• Conservation of mass
• Solution convergence
• Comparison to analytical solutions
• Comparison to laboratory experiments

As a first-principles measure of validity, a fluid model needs to conserve mass--that is, as the model progresses over time, there should always be the same amount of fluid in the model.

Another basic test of a numerical model is solution convergence. It is necessary to discretize space and time for a fluid model, and as the resolution increases (i.e., as the discretization size decreases) it is expected that the solutions converge.

Centuries of study of fluid mechanics have provided analytical solutions to many idealized wave scenarios. These are useful for comparing against numerical models. We will look at the translation of a solitary wave (a wave that propagates without changing shape).

Analytical wave theories can't describe all the ways that waves interact with complex bottom surfaces, so next we turn to laboratory experiments. Over recent decades, researchers have performed experiments in large wave tanks, generating waves for various scenarios and measuring the effects. We recreate several laboratory experiments with our model and compare the results.

[1] Yamazaki, Y., Kowalik, Z. and Cheung, K.F. (2009), Depth-integrated, non-hydrostatic model for wave breaking and run-up. International Journal for Numerical Methods in Fluids, 61: 473-497. https://doi.org/10.1002/fld.1952