https://github.com/FabricioArendTorres/burgers_equation_analytical_1d_2d

Analytical burgers equation in 1d and 2d over time. Also analytical fundamental heat and fokkerplanck equation in 3d.
https://github.com/FabricioArendTorres/burgers_equation_analytical_1d_2d

Last synced: 4 months ago
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Analytical burgers equation in 1d and 2d over time. Also analytical fundamental heat and fokkerplanck equation in 3d.

• Host: GitHub
• URL: https://github.com/FabricioArendTorres/burgers_equation_analytical_1d_2d
• Owner: FabricioArendTorres
• Created: 2023-08-29T12:01:26.000Z (almost 2 years ago)
• Default Branch: master
• Last Pushed: 2024-10-15T09:15:13.000Z (8 months ago)
• Last Synced: 2025-01-13T09:12:01.325Z (5 months ago)
• Language: Python
• Size: 1.27 MB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# Analytical solutions to time-dependent Burgers Equation in 1D and 2D

Analytical burgers equation in 1d and 2d over time. 

Also contains the analytical solution to 

a.)the fundamental heat equation 

b.) fokkerplanck equation in 3d

See `main.py` for an example on how to evaluate the solution on a spatiotemporal grid. 

The burgers implementation is based on:

`Gao, Q., and M. Y. Zou. "An analytical solution for two and three dimensional nonlinear Burgers' equation." Applied Mathematical Modelling 45 (2017): 255-270.`

## install

Requirements for conda are in the `.yml` file.

Else, you can just directly install the package with:

`pip install -e .` while being in the `pde_datasets` directory of this repo.

## Burgers 1d

![Alt text](plots/burgers_1d.png?raw=true "Burgers 1D")

## Burgers 2d

![Alt text](plots/burgers_2d_t0.00.png?raw=true "Burgers 2D")

![Alt text](plots/burgers_2d_t0.50.png?raw=true "Burgers 2D")

![Alt text](plots/burgers_2d_t1.00.png?raw=true "Burgers 2D")

## heat_3d

![Alt text](plots/heat_3d.png?raw=true "Burgers 2D")