The Coding Phase began after the 3-week long Community Bonding period. The Community Bonding period was not very intensive and acted as a good period for getting familiar and setting up the environment ready and getting prepared for the next stage.
We have set up a weekly meetup where I discuss my week’s progress with my mentors, update them on the issues faced and plan on further work.
The Coding phase started off with a meeting with project mentors. The project revolves around understanding the transition to turbulence and turbulent motion of a fluid in a cylindrical pipe.
The motion is described by the very famous Navier-Stokes equation. This is a nonlinear partial differential equation which makes them interesting and challenging at the same time.
We have generated data from the quasilinear simulations of the equation through pseudo-spectral methods. The data collected is for every point in space and time, and is a 4-Dimensional, which includes three scalars representing the velocities along the axis, along the radial and tangential directions along with the scalar pressure component.
We construct the covariance matrix and analyse the eigenvalues at each wavenumber, since we apply a fourier transform over the azimuthal dimension.
Constructing the covariance matrix, we calculate the eigenvalues of the matrix and plot them for each timestamp. The eigenvalues for a particular timestamp in transitional flow are plotted below which do not quite capture the motion, the implementation needs to be improved and modified
There are a lot of improvements to be made in the implementation which include parallelizing the code and using trapezoid rule to approximate the riemann integral for the eigenvalue computation. I would be finalizing this before moving onto actual data. I would be updating the further work in another post