Course teached as: B020994 - METODI NUMERICI PER L'ASTROFISICA Second Cycle Degree in PHYSICAL AND ASTROPHYSICAL SCIENCES Curriculum ASTROFISICA
Teaching Language
Italian
Course Content
First part: introduction to Fortran and to numerical calculus, roost-finding methods, methods for ordinary differential equations with initial values, basics of symplectic methods and n-body problems, iterative methods for partial differential equations, hyperbolic equations and conservation laws, shock-capturing methods for fluid dynamics. Second part: numerical array inversion, tridiagonal arrays, compact derivatives, semi-spectral methods, application to fluid dynamics.
W.H. Press et al. - Numerical recipes, Cambridge.
C.B. Laney – Computational gas dynamics, Cambridge.
Learning Objectives
Getting familiar with the elements of numerical analysis and computational fluid dynamics, in order to be able to write a numerical code of astrophysical interest and use numerical libraries.
Prerequisites
Basic informatics and programming. Fluid dynamics.
Teaching Methods
Frontal lectures (partly with the aid of electronic slides) and laboratory training.
Further information
Use of Fortran for coding and of Python libraries for output data visualisation.
Type of Assessment
The assessment will take into account the skills acquired during the laboratory exercises and the knowledge of the algorithms underlying the numerical methods taught by the teachers. Skills will be verified directly in the laboratory and by sending to teachers programs completed in the laboratory (or later at home). The final exam is usually oral, but upon agreement with the teachers it is possible to take a written test, immediately after the end of the course by mid-June, which will consist in writing a program similar to those already addressed in class. In case of positive outcome of the test and if the mark (out of thirty) is considered satisfactory, it is possible not to take the oral test.
Course program
First part: introduction to Fortran and to numerical calculus, roost-finding methods, methods for ordinary differential equations with initial values, basics of symplectic methods and n-body problems, iterative methods for partial differential equations, hyperbolic equations and conservation laws, shock-capturing methods for fluid dynamics and MHD. Second part: numerical array inversion, tridiagonal arrays, compact derivatives, semi-spectral methods, application to fluid dynamics.