adcell

Matlab code for solving the advection-diffusion equation for a two-dimensional incompressible autonomous cellular flow.

Installation

Clone the adcell project:

git clone https://github.com/jeanluct/adcell.git

or with SSH

git clone git@github.com:jeanluct/adcell.git

After starting Matlab, cd to the extern subfolder of the adcell project, and run mex fft2udotgrad_helper.c from within Matlab. You might need to use the -largeArrayDims option if Matlab complains. This will compile a helper function for filling the sparse matrix of the Fourier-space operator u.grad in the advection-diffusion equation.
If you cannot compile the MEX file, you'll be limited to N=31 Fourier modes in each spatial direction.
Now cd .. to come back to the root folder of the adcell project.

You're now ready to run the program!

Running

Run adcell_demo('demoX'), where X is a number from 1 to 6. The argument specifies which flow and set of parameter values are used. The banner above is the output of 'demo1', 'demo2', and 'demo3' at the final time.
You can add your own run parameters by adding a case in the switch statement at the top of adcell_demo: you can specify the diffusion coefficient (effectively the inverse Peclet number) and the number of Fourier coefficients in each dimension. N should be made larger as Diff is decreased. Another useful parameter is ks, which determines how many cells fill the domain. For ks=4, there will seem to be 8 cells in each direction, since they come in pairs.
See the examples folder for more sample code.
You can see a demo of the program with commentary in this lecture.

License

adcell is released under the MIT License. It uses jlt lib and the Fourier differentiation matrix function fourdif.m written by S. C. Reddy and J. A. C. Weideman.