# sandbox/Antoonvh/README

# My Sandbox

Welcome to the `README`

of my sandbox. This page aims to provide an overview of the projects under /sandbox/Antoonvh/. The main theme here should be geophysical flows. More specifically, I am interested in the atmospheric boundary layer. I hope you find something that sparks your interest.

-*Antoon van Hooft*-

## Physical Systems

#### Atmospheric Flows

- An Adaptive Single-Column Model for the Stable Atmospheric Boundary Layer
- Growth and decay of Convection into a Stratified Fluid over a Warm Surface
- Atmospheric waves induced by a mountain
- Shallow cumulus convection

- A rising moist bubble

- A convective boundary layer on a small planet
- A section of a subsiding shell

#### 3D Turbulence

- LES of a Vortex Cannon
- LES of Isotropic Turbulence in a Triply Periodic Box
- A Kelvin-Helmholtz instability in 3D
- The collision of two vortex rings

#### 2D Turbulence and Vortex Dynamics

- Hoek’s Ring-Vortex Generator
- The Collision of a Dipolar Vortex with a No-slip Wall
- The Structure of Dipolar Vortices
- A Kelvin-Helmholtz instability in 2D

- A Rayleigh-Taylor instability
- Vortex rebound from an opening
- Unstable flow around a Cylinder

#### Two-phase flows

- Four Droples in two binary Collisions
- Droplet splashes in a Pool
- The descent of Rain Droplets

- Liquid Planets and their Gravity Field
- A 2D Bouncing Droplet in Space
- An Axisymmetric Bouncing Droplet in Space
- Droplets resting on a hydrophobic material
- A bathtub vortex
- A plant’s capillary

#### Other

- Mixing Milk into Coffee
- Internal Waves and the Dispersion Relation
- Flow over a stress-free mountain (test)
- Laminar mixing of paint
- Flow in a toroidal geometry
- A particle-driven flow
- Liquid core convection

## Maths

- Root Finding of an Analytical Function using an Adaptive Grid
- The Fractal Dimension of the Koch Snowflake
- An example of a shape with a scale-dependent fractal dimension
- Visualization of the Mandelbrot set
- The distribution of the prime numbers along a Z-order space-filling curve:
- The locality of a Z-index curve and a regular Cartesian-style curve
- Solitary Solutions for the Korteweg-De Vries Equation

## Methods

- A Header file for the Implementation of an Eddy Viscosity Closure
- The Vreman Eddy Viscosity model
- A function that finds the location and size of the(/a) critical CFL-limited-timestep cell
- Law of the wall for flows over a rough (
`bottom`

) surface - Trace and visualize particles in a flow field
- Read x-y-z formatted binary data
- Draw isolines in
`bview3D`

- Reconstruct geometries
- Distance to volume fraction fields
- Higher-order methods and definitions
- Solution diagnostics

## Documentation

I invested some time in reading the source code to get some additional information on how the tree-grid structure is implemented in Basilisk and how Adaptivity works. To organize my toughts I wrote it down.

## Convergence tests

##### 1D Diffusion (2nd-order accurate multi-grid scheme)

- Description and the convergence rate with an equidistant grid
- Convergence rate with a locally-refined grid
- Convergence rate with decreasing refinement criteria using an adaptive grid

##### 1D Advection (2nd-order accurate Bell-Colella-Glaz scheme)

- Discription and the convergence rate with an equidistant grid
- Convergence rate with decreasing refinement criteria using an adaptive grid

#### 1D Poisson problem (2nd-order accurate Multigrid Poisson solver)

- Discription of test and the spatial convergence rate witn an equidistant grid
- Convergence rate with decreasting refinement criteria using an adapted grid based on the source term

##### Accuracy of the Refinement and Prolongation attributes

#### More tests

- The temporal accuracy for a viscous flow test case
- The spatial accuracy for a viscous flow test case
- Accuracy of the interface reconstruction of a sphere
- Calculating the curvature of a circle on various grids
- Boundary implementations

## Cases as used in *Van Hooft et al.* (2018a)

*Towards Adaptive Grids for Atmospheric Boundary-Layer Simulations*

By: J. Antoon van Hooft, Stephane Popinet, Chiel C van Heerwaarden, Steven J.A. van der Linden, Stephan R de Roode and Bas J.H. van de wiel.

In: Boundary-layer meteorology.

Vol 167, pp 421-443.

DOI: https://doi.org/10.1007/s10546-018-0335-9

In order of appearance,

- Section 2.1: Generate an example tree grid and output the relevant cells
- Section 2.2: Analysis of a data slice from a 3D turbulence simulation

- Chapter 3: DNS of the growth and decay of a convective atmospheric Boundary layer using an Adaptive grid

- Chapter 3: DNS of the growth and decay of a convective atmospheric Boundary layer in fixed-and-regular-grid mode

- Chapter 4: LES of an atmospheric boundary layer filled with a radiant smoke cloud

- Appendix 1: DNS of a lid driven cavity in two dimensions using an adaptive grid

- Appendix 1: DNS of a lid-driven cavity in two dimensions with a fixed-and-regular grid

## Cases as used in *Van Hooft et al.* (2018b)

*Adaptive Cartesian Meshes for Atmospheric Single-Column Models*

By J. Antoon van Hooft, Stéphane Popinet and Bas J.H. van de Wiel

In: Geoscientific Model Development

DOI: https://doi.org/10.5194/gmd-11-4727-2018

In order of appearance,

- Results
*Sect 3.1*, The Laminar Ekman-spiral test case; - Results
*Sect. 3.2*, The GABLS1 case; - Results
*Sect 3.3*, The GABLS2 case;

## Cases as used in *Van Hooft et al.* (2019)

*An Idealized Description for the Diurnal Cycle of the Dry Atmospheric Boundary Layer*

By J. Antoon van Hooft, Peter Baas, Maurice van Tiggelen, Cedrick Ansorge and Bas J.H. van de Wiel.

In: Journal of the Atmospheric Sciences

DOI: https://doi.org/10.1175/JAS-D-19-0023.1

In order of appearance,

- The effects of the pressure-gradient force, using a Single-Column Model (SCM).
- The effect of including a layered soil-heat storage model in the SCM.
- Large-eddy simulation of the diurnal cycle with a weak wind forcing.

## Pages for my PhD thesis

*Modeling the Atmospheric Diurnal Cycle*

In order of appearance:

- Front cover

- Ouverture: Root finding
- Entr’acte 1: The Mandelbrot set

- Chapter 2 is based on an article

- Entr’acte 2: A dipole collision with a wall

- Chapter 3 is based on an article

- Entr’acte 3: The collision of two vortex rings

- Chapter 4 is based on an article

- Entr’acte 4: Error estimation for a Poisson solver
- Encore: This section is based on the experience writing these pages

## Case as used in *Van Hooft* (2020, under review)

*A Note on the Scalar-Gradient Sharpening in the Stable Atmospheric Boundary Layer*

By: J. Antoon van Hooft

Under review at: Boundary-Layer Meteorology

Scalar-gradient sharpening by the self advection of a dipolar vortex.

## Miscellaneous pages

- Playing games with Basilisk
- A cautionary note on the simulation of a sharp inversion layer
- A cautionary note on using the Navier-Stokes solver without a properly initialized/restored pressure field
- A cautionary note on using surface tension in combination with grid adaptivity
- Evaluating a line integral on a tree grid
- Experimental adaptivity pages
- The Helmholtz filter

## Contact

If you like to discuss a specific topic, feel free to e-mail me: j.a.vanhooft-{\mathcal{A}}-tudelft.nl