This code implements spectral filtering and Gibbs complimentary basis re-expansion, as outlined in the paper Spectral Methods for Hyperbolic Problems by Gottlieb and Hesthaven.
It is part of an end-semester project, which you can read more about here.
Download or clone this repository and then activate your environment before running
pip install -r requirements.txtto install the required packages, in case they are not already present.
python main.py -hwill show the list of options.
| Flag | Explanation |
|---|---|
-N |
Number of grid points and Fourier modes (can be used multiple times) |
--pde |
Whether to solve the linear advection or Burgers' equation |
--ggb |
Plot the re-expansion of Fourier coefficients in the basis of Gegenbauer polynomials |
--Lambda |
When --ggb is enabled, the value of Lambda to use (sometimes referred to as alpha) for the Gegenbauer polynomials. Must be used as many times as -N. |
--exact |
Path to the file containing the exact solution for the specified combination of PDE, initial condition, at final time. |
The Burgers' equation computes the right solution, but at a wrong speed.