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 can find something that interests you.

-Antoon van Hooft-

Physical Systems

Atmospheric Flows

• An Adaptive Mesh Single Column Model for the Stable Atmospheric Boundary Layer
• Growth and decay of Free Convection into a Linearly Stratified Fluid over a Surface with a Fixed Buoyancy
• Mountain waves
• Shallow cumulus convection

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
• A Lid-Driven Cavity in Two Dimensions
• The Collision of a Lamb-Chaplygin Dipolar Vortex with a No-slip Wall
• The Structure of Dipolar Vortices
• A Kelvin-Helmholtz instability in 2D
  
• Subsequently colliding vortex pairs
• A Rayleigh-Taylor instability

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

Other

• Mixing Milk into Coffee
• Internal Waves and the Dispersion Relation

Embedded Boundary examples

• Vortex Rebound from an Opening
• Unstable flow around a Cylinder
• Flow over a stress-free Mountain (test)
• Mixing of Paint

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
  1. A zoom in on a specific location
  2. A high resolution image of the entire set
• The distribution of the prime numbers along a Z-order space-filling curve:
  1. In two dimensions
  2. In three dimensions
     
• 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
• Solution diagnostics
  1. A vertical-averaging profiling function
  2. A generic interface-averaging profiling function
  3. Diagnose solution fields along a 2D interface
  4. A function that computes a second order longitudional structure function of a vector field

Convergence tests

Some tests were carried out to get a feeling for convergence rates when using grid adaptivity.

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-Cotella-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

• In 1D
• In 2D
• In 3D

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
  1. A comparison of four straight and grid-aligned methods
  2. A comparison of three cylinderical-geometry implementations

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.

• The Tree-Grid structure in Basilisk
• The Wavelet Based Adaptive Grid Algorithm

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;
  1. using a fixed and equidistant grid
     
  2. using an adaptive grid
• Results Sect. 3.2, The GABLS1 case;
  1. using an adaptive grid
  2. using a fixed and equidistant grid
     
• Results Sect 3.3, The GABLS2 case;
  1. using an adaptive grid
  2. using a fixed and equidistant grid

Miscellaneous pages

• 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
• A bview example
• Create and display an animated .gif and .mp4 movie in the sandbox
• Evaluating a line integral on a tree grid
• A discussion on Second order interpolation at Resolution Boundaries
• Additional attributes for 3rd order interpolation at resolution boundaries
• An example on how and when to employ higher order accurate definition of ghost / Halo cells
• A 2D test of the 3rd order accurate interpolation techniques at resolution boundaries using the Lamb-Dipole example
• Experimental adaptivity pages
  1. A (test of a) flexible wavelet-based adaptation algorithm
  2. A space-time adaptive solver
  3. Adaptively computing a maximum level
  4. A very flexible adaption function
  5. An adaptivite method on an equidistant grid

Contact

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