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M4132 Computational astrophysics
Aims:
Some of the most powerful computational methods for astrophysics are particle methods. These range from the n-body calculations, where systems of stars are represented by a large number of particles, which move under the gravitational forces, to particle methods for gas dynamics. At Monash we have developed a powerful, flexible particle method called Smoothed Particle Hydrodynamics (SPH). In this course we will show how this method can be used for the simulation of colliding stars, the fragmentation of gas clouds and the dynamics of galaxies. Along the way you will learn how to simulate shock waves and metal-metal impacts (needed for cometary impact on the earth). Because of its flexibility, and the ease with which complicated physics can be included, this particle method has numerous applications in geophysics and in industrial processes.
Syllabus:
How to represent a continuous fluid by particles.
The continuity and acceleration equation in the particle representation.
Wave motion and dispersion induced by the discrete particles.
Time stepping algorithms.
The energy equation.
Artificial viscosity and shockwaves.
Questions of accuracy.
How to calculate the gravitational field with a tree code.
We make a polytrope, oscillate it and put into orbit.
How to set up and evolve an accretion disk.
Relation to Riemann methods which look good but fail.
How to treat several fluids including dusty gas.
How to simulate a breaking dam and a tank with several fluids (it's easy).
More on time stepping algorithms especially the implicit case.
Is relativistic fluid dynamics that hard? We explore some SPH formulations
Recommended texts: This topic is so new a text book has not been written. References to extensive review articles will be provided.
Lecturer: Joe Monaghan
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