Properties and equations of fluids: Lagrangian and Eulerian views of fluid flow; equations of fluids (continuity equation, Euler’s equation, conservation of energy), equations of state (including polytropic models); application to astrophysical systems.
Static solutions to fluid equations: hydrostatic equilibrium, application to modelling stellar structure.
Forces acting on fluids: viscosity (Navier-Stokes equation), gravity and Poisson’s equation, magnetic fields, source terms (e.g., mass loading, heating, cooling), and their roles in astrophysical systems.
Accretion and shocks: Bernoulli equation and Bondi accretion, continuous shocks, Rankine-Hugoniot conditions, astrophysical applications (e.g., active galactic nuclei, supernovae remnants, radio galaxies).
Fluid instabilities: convection, sound waves in fluids, instabilities at fluid boundaries (Rayleigh-Taylor and Kelvin-Helmholtz instabilities), Jeans instability and star formation.
Eulerian approaches to fluid simulation: finite difference methods, von Neumann stability analysis, Courant-Friedrichs-Lewy stability criterion, stiff equations and implicit methods, the shock tube problem and Godunov’s method, applications in astrophysics.
Lagrangian approaches to fluid simulation: N-body codes, tree codes, force softening, smoothed particle hydrodynamics, applications in astrophysics.
Limitations of astrophysical simulations: sub-grid physics, semi-analytic models, the effects of spatial and temporal resolution limits on the interpretation of simulation results.
After completing this module students are expected to be able to:
Explain and derive the fundamental equations that describe fluid motion.
Explain the differences between Eulerian and Lagrangian approaches to fluid simulation, and the advantages and disadvantages of each.
Understand the relationship between the fluid equations and the equations of stellar structure.
Evaluate situations in which the behaviour of fluids in astrophysical systems is significantly affected by external forces, such as viscosity, magnetic fields, heating/cooling, or mass loading, and describe these in terms of modifications of the fluid equations.
Apply the theory of Bondi accretion to astrophysical systems and calculate accretion rates.
Identify instabilities and shocks in astrophysical observations or simulations, and describe and explain their causes and effects on the system in question.
Evaluate the stability of various finite difference schemes.
Describe and explain the implementation of various N-body approaches to fluid simulation.
Discuss critically the limitations of numerical methods applied in astrophysical simulations.