Nicholas Vieira
Python 3.7
Collaborator: Sabrina Berger
================================================
This repository contains the following scripts which constitute a library of functions:
differencing.py
donor_cell.py
These scripts are called by the following 3 scripts:
Q3_advection.py
Q4_diffusion_advection.py
Q5_1Dhydro.py
The first of which provides the solution to question #3 of the assignment, and so forth.
All scripts can be run via the command line via e.g.
>>> python Q3_advection.py
With the appropriate dependencies, i.e.,
- matplotlib 3.0.3
- numpy 1.16.2
[5] 1-Dimensional Hydro solver
As the amplitude of the Gaussian perturbation increases, the solution becomes increasingly unstable. In particular:
- For a density with baseline offset
OFFSET=100.0
and perturbation amplitudeAMP=0.5
, the solution is stable. - For a density with the same base offset and a perturbation amplitude of
AMP=10.0
, the solution blows up, and the amplitude of the sound waves tends to infinity. The hydro solver eventually crashes under these conditions.
A shock begins to appear depending on the ratio between dx and dt. In the scheme we used, no viscosity is explicitly included, but we have incurred a "numerical viscosity" due to the approximations used in the finite differencing steps. This numerical viscosity is proportional to dx**2 / dt, and so it is this quantity which sets the width of the shock (Equation (15)).