Alfvén waves in one dimension
Fortran code that simulates how nonlinear interaction deforms Alfvén waves in a plasma, with a LaTeX report. I did it on my own in one month, between August and September 2022.
The problem
Alfvén waves are magnetohydrodynamic waves. In the Elsässer variables, Z+ and Z-, they are two waves travelling in opposite directions: if the equation were linear they would cross without disturbing each other, with the nonlinear terms they deform each other. I wanted to see how, by solving the equations myself.
How it works
- 01
The scheme
Compact finite differences with a Lele filter; the derivatives require solving tridiagonal and pentadiagonal systems. About 525 lines of Fortran in separate modules.
- 02
The report
It derives the equations in the Elsässer variables and discusses the results (title: "Nonlinear effects on Alfvén waves in one dimension").
- 03
The plots
Built with gfortran and a Makefile; the plots are made in Python with matplotlib.
What I did
Everything: the code, the report and the plots. 21 commits.
Limits
It is study code, not an application. I did not compare the results with other codes.
Stack: Fortran (gfortran), Python and matplotlib, LaTeX.