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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

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 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
• 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

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

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
• Draw isolines in bview3D
• 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

Cases as used in Van Hooft et al. (Under review)

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. Under review for the Journal of the Atmospheric Sciences

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.

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{A}}-tudelft.nl

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