The complexity in Astrophysics
Will Lecture 2026

This course will introduce the basic concepts of hydrodynamics and how they are applied to astrophysical simulations.

Lectures

Suggested Literature

• Principles of Astrophysical Fluid Dynamics, C. J. Clarke and R. F. Carswell
• Simulation Techniques for Cosmological Simulations, K. Dolag, S. Borgani, S. Schindler, A. Diaferio and A. M. Bykov
• Density Estimation for Statistics and Data Analysis, B. W. Silverman
• Theoretical Fluid Dynamics, A. Feldmeier
• Computational Methods for Astrophysical Fluid Flow, R. J. LeVeque, D. Mihalas, E. A. Dorfi and E. Mueller
• The Encyclopedia of Cosmology, Volume 2: Numerical Simulations in Cosmology, Kentaro Nagamine (ed.)
• Hydrodynamic methods and sub-resolution models for cosmological simulations, M. Valentini and K. Dolag

Lecture Plan

• 09.03.26 (13:30-15:00), L1: Introduction into Concepts of Fluid Dynamics
  Mainly based on Chapters 1 and 2 of Principles of Astrophysical Fluid Dynamics
• 10.03.26 (08:30-10:00), L3: Energy EQ and Density Estimates
  Mainly based on Chapter 3.2 of Simulation Techniques for Cosmological Simulations
  and Chapters 1–3 of Density Estimation for Statistics and Data Analysis
• 10.03.26 (13:30-15:00), L2: Eulerian Hydrodynamics and the Riemann Problem
  Mainly based on Chapter 3.1 of Simulation Techniques for Cosmological Simulations
• 11.03.26 (08:30-10:00), L4: Sound Waves
  Mainly based on Chapters 6.1 and 6.2 of Principles of Astrophysical Fluid Dynamics
• 11.03.26 (13:30-15:00), L5: Shocks and Bastwave
  Mainly based on Chapters 7 and 8 of Principles of Astrophysical Fluid Dynamics
• 12.03.26 (08:30-10:00), L6: Bernoulli’s equation, Laval nozzle & some notes on heat transport and viscosity
  Mainly based on Chapters 9.1 and 9.2 of Principles of Astrophysical Fluid Dynamics
• 12.03.26 (13:30-15:00), L7: Sub-Grid Physics (star-formation)
  Mainly based on Chapters 4.1 and 4.2 of Simulation Techniques for Cosmological Simulations
  as well as parts of following publications: Sections 3.1 and 4.2 of arXiv:astro-ph/9509107 and Sections 2, 3, and 4 of arXiv:astro-ph/0206393.
• 13.03.26 (08:30-10:00),, L8: History of cosmology, galaxy clusters and simulations
  Some historical notes on our understanding of the cosmos,
  some notes on how galaxy clusters help us to understand our universe,
  some insights on how cosmological simulations are done.Slides.

Tutorials

In this class you will be required to write small computer programs to set up and analyze various interesting hydrodynamic flows. The simulations themselves will be done with a given hydrodynamics code and you will be given access to central computers to perform the simulations and the analysis of them. This will require some effort and lots of experimentation from your side. But keep in mind that programming is not the main aspect of these tutorials — understanding the physics of the different experiments is.

Each of the tutorials needs some preparation based on short, general questions related to some aspects of the current exercise set and the related physical and numerical issues. You are expected to have prepared yourself by answering some key questions beforehand.
During the tutorials you will work on setting up the test problems and performing the hydrodynamic simulations.

You can use your own laptop, where we provide a container with all you need. It will be requited to setup your laptops to handle containers. We will provide soon more informations and also use the first tutorial to help you to get everything running. You need to be familiar with

• a text editor to edit programs (such as emacs, nano or vim)
• a program to produce graphs (for example Python+matplotlib)

Tutorial schedule

• 09.03.26 (15:15-16:45), T1: Introduction Computer: container, shell, command-line, editing, compiling, running, reading-data, plotting
• 10.03.26 (10:15-11:45), T2: Density estimates
• 10.03.26 (15:15-16:45), T3: The Riemann problem
• 11.03.26 (10:15-11:45), T4: Propagating sound waves
• 11.03.26 (15:15-16:45), T5: Blast wave
• 12.03.26 (10:15-11:45), T6: Flow through a Nozzle
• 12.03.26 (15:15-16:45), T7: Simulating a disk galaxy and reproducing the SK relation
• 13.03.26 (10:15-11:45), T8: Vizualising Galaxies with Splotch