HW-ProjectIV

Repository by Harry Wiffen for Project IV: Stokes and the Brinkmanlets, submitted for the degree of Master of Mathematics at Durham University.

This repository contains all code used in Stokes and the Brinkmanlets. Code is written in Python and R.

The complete dissertation report can be found at Stokes_and_the_Brinkmanlets.pdf

Consistent colour maps are used throughout to distinguish simulation types (from matplotlib):

• Stokes flows: 'cool'
• Brinkman flows: 'winter'
• Magnetised flows: 'autumn'

Folder Structure

HTML_interactive_plots/

3D interactive simulation results, saved as .HTML files. Files were written using write_html from the plotly package.

Note: Only one plot of each simulation type is included, due to GitHub file size limits. Any other plots can be produced directly using interactive_online_plots.py.

npy_output_files/

Raw simulation results from all models, saved as .npy files. Can be imported into visualisation scripts.

Note: Many longer simulations are excluded, due to GitHub file size limits.

Simulation_scripts/

Scripts for running simulations and saving outputs as .npy files. Simulation parameters must be specified:

• optimised_stokes_save_to_npy.py Simulates a falling particle cloud in Stokes flow.
• optimised_brinkman_save_to_npy.py Simulates a falling cloud in Brinkman flow.
• optimised_magnetised_save_to_npy.py Simulates a falling cloud in a magnetised Brinkman flow.
• articulated_body_save_to_npy.py Simulates a falling 3D articulated body in Brinkman flow.

Main_visualisation_scripts/

Scripts for visualising simulation results. Simulation parameters must be specified, and the corresponding .npy file is then imported:

• interactive_online_plots.py Produces an online, interactive 3D plot with plotly and saves it as an .HTML file.
• multi_frame_graphs.py Creates holistic multi-frame visualisations. Option to also return separate zoomed-in frames.

Spread_analysis/

Scripts for analysing and visualising particle dispersion. Raw data is calculated using Python and saved as a .csv file, to be imported into R for visualisation:

• spread_analysis_save_to_csv.py Processes simulation data and saves particle spread data as .csv.
• Raw_spread_data_vs_LLRE.R Plots raw dispersion data with the local linear regression estimator (LLRE), for visual comparison.
• Stokes_spread_analysis.R LLRE spread plots for Stokes flow simulations.
• Brinkman_spread_analysis.R LLRE spread plots for Brinkman flow simulations.
• Magnetised_spread_analysis.R LLRE spread plots for magnetised flow simulations.

Misc_visualisation_scripts/

Additional visualisation scripts:

• scalar_blobs_visualisation.R Plots multiple Gaussian scalar blob functions, with the Dirac delta measure for comparison.
• regularised_soln_blob_heatmaps.R Heatmaps of regularised Brinkman blob solutions for different width parameters.
• streamlines_fundamental_vs_regularised_brinkman.py Compares streamlines of fundamental and regularised Brinkman solutions, with a visual representation of the force concentrations.

License

This project is licensed under the MIT License.