mikejmnez/adv_diff_supplemental_materials

Supplemental materials for the JFM paper "Advection Diffusion Equation: An Exact Solution..."

Adv_Diff_Supplemental_Materials

Supplemental materials for the JFM paper "Advection Diffusion Equation: An Exact Solution..."

How to run remotely

Click on the Binder link above. It takes some time, while installing dependencies and getting the correct environment ready.

How to run locally

on OSX/Linux:

On the terminal, clone this repository

git clone https://github.com/Mikejmnez/Adv_Diff_Supplemental_Materials.git

Navigate into main directory and install environment

conda env create -f environment.yml

Once the environment is install, activate it

conda activate Advection_Diffusion

Then navivate into Advection_Diffusion directory and run the interactive notebooks

cd Advection_Diffusion jupyter lab

Notebooks:

• Mathieu_Eigenvalue.ipynb: Compute and display Mathieu functions, their eigenvalues, Fourier expansions, and various identities.
• Shear_Dispersion_Average_Gaussian.ipynb: Compute the cross-channel average solution for a narrow Gaussian initial condition.
• Adv_Diff_IVP_Animation_01.ipynb: Full time-dependent solution for a cosine initial condition with wavenumber k. The wavenumber k can be modified by the used to better understand the behavior of solutions with different wavelengths.
• Adv_Diff_IVP_Animation_02.ipynb: Full time-dependent solution for a Gaussian initial condition, plus the average solution.
• Ellipse_Approx_Eigenvalues.ipynb: Elliptical parametrization of the Mathieu eigenvalue dependence on parameter q.