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.<\/p>\n
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, P\u00b3M).<\/p>\n
Hands-on exercises form an integral part of the course. Students will work on small programming assignments\u2014ranging 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.<\/p>\n
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.<\/p>\n
[\/et_pb_text][et_pb_text _builder_version=”4.27.4″ _module_preset=”default” header_2_font_size=”30px” global_colors_info=”{}”]<\/p>\n
Reading List<\/h2>\n
[\/et_pb_text][et_pb_text _builder_version=”4.27.4″ _module_preset=”default” global_colors_info=”{}”]<\/p>\n
- \n
- Numerical Recipes: The Art of Scientific Computing.<\/em> Cambridge Univ. Press. Book available online<\/a><\/li>\n
- Gravitational N-body Simulations. <\/em>S. Aarseth. Cambridge Univ Press.<\/li>\n
- Computer Simulations using Particles<\/em>. Hockney & Eastwood.<\/li>\n
- Riemann Solvers and Numerical Mtehods for Flui Dyamics. E. Toro Book available online.<\/a><\/li>\n
- An\u00e1lisis Num\u00e9rico con Aplicaciones<\/em>. C.F. Gerald y P.O. Wheatley. Editorial Addison-Wesley.<\/li>\n
- An\u00e1lisis Num\u00e9rico<\/em>. R.L. Burden, J. Douglas Faires. Editorial International Thomson Editores.<\/li>\n
- C\u00e1lculo Num\u00e9rico.<\/em>B. Carnahan, H.A. Luther y J.O. Wilkes. Editorial Rueda.<\/li>\n
- Elementary Numerical Analysis<\/em>. Kendall Atkinson. John Wiley and Sons.<\/li>\n
- Computational Gas Dyanamics<\/em>. C. B. Laney. Cambridge Univ. Press.<\/li>\n
- Computational Methods for Astrophysical Fluid Flows<\/em>. Le Veque, et al. Springer-Verlag.<\/li>\n
- Gravitational N-body Problem<\/em>. M. Lecar. Kluwer.<\/li>\n
- Numerical Methods in Astrophysics<\/em>. Bodenheimer. Taylor & Francis<\/li>\n<\/ul>\n
[\/et_pb_text][et_pb_text _builder_version=”4.27.4″ _module_preset=”default” header_2_font_size=”30px” global_colors_info=”{}”]<\/p>\n
Teaching Plan Information<\/h2>\n
[\/et_pb_text][et_pb_image src=”https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-21-3-scaled.png” title_text=”Asignaturas m\u00e1ster (21)” url=”https:\/\/drive.google.com\/file\/d\/11piyFbCyad9RmZtmTtRrTRi-LQPZviyx\/view” url_new_window=”on” _builder_version=”4.27.4″ _module_preset=”default” width=”50%” max_width=”50%” module_alignment=”center” global_colors_info=”{}”][\/et_pb_image][et_pb_text _builder_version=”4.27.4″ _module_preset=”default” header_2_font_size=”30px” custom_margin=”50px||||false|false” global_colors_info=”{}”]<\/p>\n
Course Schedule<\/h2>\n
[\/et_pb_text][et_pb_image src=”https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-20-4-scaled.png” title_text=”Asignaturas m\u00e1ster (20)” url=”https:\/\/drive.google.com\/file\/d\/1xBMn7MrIvl8NAEx0kmV83tDH-cMXrWRu\/view” url_new_window=”on” _builder_version=”4.27.4″ _module_preset=”default” width=”50%” max_width=”50%” module_alignment=”center” global_colors_info=”{}”][\/et_pb_image][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"
Academic TeamCourse ContentType: Optional\u2013 AC Track \u2013 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, […]<\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"\n
Academic Team<\/h2>\n\n\n\n
![\"\"](\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-28-1024x576.png\")
<\/a><\/figure>\n\n\n\n![\"\"](\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-29-1024x576.png\")
<\/a><\/figure>\n\n\n\n![\"\"](\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-31-1024x576.png\")
<\/a><\/figure>\n\n\n\n![\"\"](\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-32-1024x576.png\")
<\/a><\/figure>\n\n\n\nCourse Content<\/h2>\n\n\n\n
Type: Optional\u2013 AC Track \u2013 3rd Trimeste<\/strong>r<\/p>\n\n\n\n
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.<\/p>\n\n\n\n
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, P\u00b3M).<\/p>\n\n\n\n
Hands-on exercises form an integral part of the course. Students will work on small programming assignments\u2014ranging 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.<\/p>\n\n\n\n
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.<\/p>\n\n\n\n
Reading List<\/h2>\n\n\n\n
- \n
- Numerical Recipes: The Art of Scientific Computing.<\/em> Cambridge Univ. Press. Book available online<\/a><\/li>\n\n\n\n
- Gravitational N-body Simulations. <\/em>S. Aarseth. Cambridge Univ Press.<\/li>\n\n\n\n
- Computer Simulations using Particles<\/em>. Hockney & Eastwood.<\/li>\n\n\n\n
- Riemann Solvers and Numerical Mtehods for Flui Dyamics. E. Toro Book available online.<\/a><\/li>\n\n\n\n
- An\u00e1lisis Num\u00e9rico con Aplicaciones<\/em>. C.F. Gerald y P.O. Wheatley. Editorial Addison-Wesley.<\/li>\n\n\n\n
- An\u00e1lisis Num\u00e9rico<\/em>. R.L. Burden, J. Douglas Faires. Editorial International Thomson Editores.<\/li>\n\n\n\n
- C\u00e1lculo Num\u00e9rico.<\/em> B. Carnahan, H.A. Luther y J.O. Wilkes. Editorial Rueda.<\/li>\n\n\n\n
- Elementary Numerical Analysis<\/em>. Kendall Atkinson. John Wiley and Sons.<\/li>\n\n\n\n
- Computational Gas Dyanamics<\/em>. C. B. Laney. Cambridge Univ. Press.<\/li>\n\n\n\n
- Computational Methods for Astrophysical Fluid Flows<\/em>. Le Veque, et al. Springer-Verlag.<\/li>\n\n\n\n
- Gravitational N-body Problem<\/em>. M. Lecar. Kluwer.<\/li>\n\n\n\n
- Numerical Methods in Astrophysics<\/em>. Bodenheimer. Taylor & Francis<\/li>\n<\/ul>\n\n\n\n
Teaching Plan Information<\/h2>\n\n\n\n
![\"\"](\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-21-2-1024x576.png\")
<\/a><\/figure>\n\n\n\nCourse Schedule<\/h2>\n\n\n\n
![\"\"](\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-20-2-1024x576.png\")
<\/a><\/figure>\n\n\n\n<\/p>\n","_et_gb_content_width":"1080","footnotes":""},"categories":[28,32],"tags":[],"class_list":["post-1451","post","type-post","status-publish","format-standard","hentry","category-afc-track","category-optional-en-afc-track"],"_links":{"self":[{"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1451","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/comments?post=1451"}],"version-history":[{"count":10,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1451\/revisions"}],"predecessor-version":[{"id":2379,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1451\/revisions\/2379"}],"wp:attachment":[{"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/media?parent=1451"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/categories?post=1451"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/tags?post=1451"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- Gravitational N-body Simulations. <\/em>S. Aarseth. Cambridge Univ Press.<\/li>\n\n\n\n
- Gravitational N-body Simulations. <\/em>S. Aarseth. Cambridge Univ Press.<\/li>\n