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 topics here reflect my interest in fluid-flow phenomena, numerical methods, popular maths and (Basilisk-)programming exercises. 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
• The diurnal cycle of the atmosphere

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
• Untying a vortex knot

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

Multiphase 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
• A Droplet water slide

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
  
• Tesla’s valve

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
• A Hilbert curve grid iterator
• Solitary Solutions for the Korteweg-De Vries Equation
• Solving an implicit integral equation
• The Helmholtz filter

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
• 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
  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

• Generic Particle functions
  • Flow tracers
    • vof-interface-bounded tracers
  • Inertial particles
    • Cosmological dynamics
    • Stokes particles
  • A bview function for plotting particles
• Ray-casting visualization
• A Robin/mixed boundary condition
• 5-point 8th-order accurate finite-difference derivatives
• A 4th-order accurate solver for the Navier-Stokes equations

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

Other READMEs

• Overview of pages used in published articles
  
• Tests for numerical schemes
  
• Overview of pages for the Plantenna project

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
  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
• Encode a movie on an octree
• Hilbert-order MPI-domain decomposition on trees
• Download sandbox contents without darcs

Contact

If you like to discuss a specific topic, feel free to e-mail me: j.a.v.hooft-{\mathcal{A}}-gmail.com. I also have a website.