Academic Team

Course Content

Type: Optional– AC Track – 3rd Trimester

This course provides the theoretical and practical foundations to model astrophysical phenomena using numerical simulations. Students will be introduced to the principles of computational astrophysics and high-performance computing, gaining proficiency in scientific programming and the use of advanced numerical techniques.

The programme covers numerical integration methods, the solution of ordinary and partial differential equations, and their application to key physical processes: gravitational dynamics, N-body systems, (magneto-)hydrodynamics, and gas dynamics. Both Eulerian and Lagrangian approaches are presented in detail, including state-of-the-art algorithms such as Particle-Mesh (PM), Adaptive Mesh Refinement (AMR), Smoothed Particle Hydrodynamics (SPH), tree codes, and hybrid schemes (treePM, P³M).

Hands-on exercises form an integral part of the course. Students will work on small programming assignments—ranging from visualising the Mandelbrot set to implementing integration schemes for gravitational two-body systems, and developing a 1D SPH code for gas dynamics. A final project allows participants to either build a tailored simulation tool or employ a professional astrophysical code to investigate systems such as planetary configurations, stellar clusters, or galaxy formation.

By the end of the course, students will not only master the computational methods at the core of modern astrophysics but also acquire the skills needed to run and analyse large-scale simulations on high-performance computing systems, preparing them for research in both theoretical and observational contexts.

Reading List

• Numerical Recipes: The Art of Scientific Computing. Cambridge Univ. Press. Book available online
• Gravitational N-body Simulations. S. Aarseth. Cambridge Univ Press.
• Computer Simulations using Particles. Hockney & Eastwood.
• Riemann Solvers and Numerical Mtehods for Flui Dyamics. E. Toro Book available online.
• Análisis Numérico con Aplicaciones. C.F. Gerald y P.O. Wheatley. Editorial Addison-Wesley.
• Análisis Numérico. R.L. Burden, J. Douglas Faires. Editorial International Thomson Editores.
• Cálculo Numérico. B. Carnahan, H.A. Luther y J.O. Wilkes. Editorial Rueda.
• Elementary Numerical Analysis. Kendall Atkinson. John Wiley and Sons.
• Computational Gas Dyanamics. C. B. Laney. Cambridge Univ. Press.
• Computational Methods for Astrophysical Fluid Flows. Le Veque, et al. Springer-Verlag.
• Gravitational N-body Problem. M. Lecar. Kluwer.
• Numerical Methods in Astrophysics. Bodenheimer. Taylor & Francis

Teaching Plan Information

Course Schedule