nvieira-mcgill / phys643-astrofluids-ps5

Simple finite differencing/hydrodynamics codes developed for the class PHYS643: Astrophysical Fluids at McGill University, taught by Professor Eve Lee in Fall of 2020.

Nicholas Vieira

Python 3.7

Collaborator: Sabrina Berger

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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 amplitude AMP=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)).