## Introduction
This folder is for examples in Basilisk compiled by Lily Battershill (Lily.Battershill@niwa.co.nz). 

## Navier-Stokes "three-phase" model: pyroclastic density current generated tsunami 

The tsunami generation potential of pyroclastic density currents (PDCs) entering the sea is poorly understood, due to limited data and observations. Thus far, tsunami generation by PDCs has been modeled in a similar manner to tsunami generation associated with landslides or debris flows, using two-layer depth-averaged approaches. Using the adaptive partial differential equation solver Basilisk and benchmarking with published laboratory experiments, this work explores some of the important parameters not yet accounted for in numerical models of PDC-generated tsunamis. We use assumptions derived from experimental literature to approximate the granular, basal flow component of a PDC as a dense Newtonian fluid flowing down an inclined plane. This modeling provides insight into how the boundary condition of the slope and the viscosity of the dense granular-fluid influence the characteristics of the waves generated.

The setup is based on the experimental
geometry of [Bougouin et al., 2020](#bougouin2020), where a laboratory
fluidised granular flow runs down a ramp and into water. We assume the fluidized grains from the experiments of [Bougouin et al., 2020](#bougouin2020) to behave as a continuum. This takes the form of a dense, viscous and incompressible Newtonian fluid. The dense fluid and the water are assumed to be miscible with one another, but immiscible with air: they are separated from the air by a sharp interface. Surface tension is assumed to have negligible effect on interaction dynamics and wave propagation, due to the contrast of scales. Please see [fluidised_flow.c](http://basilisk.fr/sandbox/lbattershill/pdc_final/fluidised_flow.c) for details of implementation.

We update [conserving.h](http://basilisk.fr/src/navier-stokes/conserving.h) (see  [myconserving.h](http://basilisk.fr/sandbox/lbattershill/pdc_final/myconserving.h)) to implement momentum-conserving VOF advection of the velocity components for the two-phase Navier–Stokes solver, with the addition of a density tracer on one side of the interface. This provides an alternative to a more classic "three phase" approach, where the phases are seperated by interfaces. 

## Multi-Layer model: pyroclastic density current generated tsunami
The setup is dimensionless and based on the experimental
geometry of [Bougouin et al., 2020](#bougouin2020), where a laboratory
fluidised granular flow runs down a ramp and into water.
We use assumptions from experimental literature to approximate the fluidized grains as a continuum, which takes the form of a dense, incompressible fluid. This assumption is confirmed to be adequate in the context of wave generation, by the numerical work of [Battershill et al.,
2021](#battershill2021). This [non-hydrostatic multi-layer numerical model](http://basilisk.fr/src/layered/nh.h) assumes the dense fluid and the water to be miscible with one another. We consider only small variations in density between the granular-flow and the water, and we therefore justify the [Boussinesq buoyancy approximation](http://basilisk.fr/src/layered/dr.h).

* [Layered density version](http://basilisk.fr/sandbox/lbattershill/multilayer-slide/slide_layered.c) We simulate a dense layer at base of flow, overlayed by a lighter layer. Note: the reference to density layering is different from the vertical disretisation of the multilayer scheme.
* [Single density version](http://basilisk.fr/sandbox/lbattershill/multilayer-slide/slide.c) We simulate a dense flow (of a single density) propogating into water.

/**
## References

~~~bib
@article{bougouin2020,
  title={Impact of fluidized granular flows into water: implications for tsunamis generated by pyroclastic flows},
  author={Bougouin, Alexis and Paris, Raphael and Roche, Olivier},
  journal={Journal of Geophysical Research: Solid Earth},
  volume={125},
  number={5},
  pages={e2019JB018954},
  year={2020},
  publisher={Wiley Online Library},
  doi={10.1029/2019JB018954}
}

@article{battershill2021,
  title={Numerical simulations of a fluidized granular flow entry into water: insights into modeling tsunami generation by pyroclastic density currents},
  author={Battershill, Lily and Whittaker, Colin and Lane, Emily and Popinet, Stephane and White, James and Power, William and Nomikou, P},
  year={2021}
}
~~~
*/