Numerical Magnetohydrodynamics
Prerequisiti
First year of PHD, possible also for advanced Masters students. Prerequisites: programming in python and/or fortran, c, c++
Programma
This course provides an advanced overview of the numerical methods used to model magnetized fluids, especially (although not exclusively) in the field of Astrophysics. It is primarily hands-on, requiring code development, ploting and analysis of the results.
Course Content:
- Introduction to space plasmas: properties and characterization.
- Guiding-center equations for moving charges in an electromagnetic field.
- Introduction to the equations of MHD and their properties.
- MHD waves.
- Solving the MHD equations numerically: conserving schemes.
- The Riemann problem.
- Introduction to the RAMSES MHD code.
- MHD instabilities: applications using the RAMSES code.
- Blast waves: applications using the RAMSES code.
- MHD turbulence: applications using the RAMSES code.
Obiettivi formativi
Upon completion of this course, students will be able to:
- Understand the basics of plasma physics and the applicability of the MHD approximation.
- Develop code that calculates the trajectories of charged particles in an EM field.
- Develop code that solves the hydrodynamics equations in one dimension.
- Use a state-of-the-art, parallelized 3D MHD code for advanced problems.
- Design, execute and analyze an MHD simulation.
Riferimenti bibliografici
"Riemann Solvers and Numerical Methods for Fluid Dynamics", E. Toro