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Ciclo di seminari: Metodi Numerici per le Leggi di Conservazione Iperboliche
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Seminars on "Numerical Methods for Hyperbolic Conservation Laws"
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Academic year 2015/2016
- Teacher
- Prof. Matteo Semplice (Lecturer)
- Type
- A scelta dello studente
- Course disciplinary sector (SSD)
- MAT/08 - analisi numerica
- Delivery
- Tradizionale
- Language
- Inglese
- Type of examination
- Orale
- Prerequisites
- Basics of numerical analysis.
The courses of the LT in Mathematics will give sufficient background to understand the course, but knowledge of the topics covedered in Istituzioni Di Analisi Numerica (LM in Mathematics) would be an advantage. - Oggetto:
Sommario del corso
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Course delivery
Lezione frontale in aula (12 ore) e programmazione assistita dal docente in laboratorio informatico (4 ore).
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Learning assessment methods
Project work and oral exam. Please contact the teacher to agree on a topic for the project.
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Program
(Dal 13/10/2015) 8 incontri, al martedì dalle 10:30 alle 12:30 (Aula 5/ Info2).
La frequenza permette di ottenere fino a 3 firme per il corso MathLab.
L1(13/10, Aula 2): Hyperbolic conservation laws, strong form, finite volume form, Rankine-Hugoniot conditions and Hugoniot locus
L2(20/10, Aula 2) solution of linear equations and systems using characteristics, domain of dependence of the exact solution; upwind scheme for the linear transport equation, von Neumann analysis
L3(27/10, Aula 2) CFL condition; Riemann problems for convex fluxes, entropy; conservative schemes, Local Lax Friedrichs scheme, (Lax Wendroff theorem?)
L4(03/11, Info 2): Exercises in MatLab (Room Info2)
L5(10/11, Aula 2): second order schemes, Harten's theorem, slope limiters, ENO/WENO reconstruction
L6(17/11, Aula 2): schemes for systems: Hugoniot locus, Riemann solvers, LLF scheme
L7(24/11, Info 2): Exercises in MatLab (Room Info2)
L8(03/12, Aula 2): schemes for balance laws: well-balanced schemes for the shallow water equations
Suggested readings and bibliography
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The best reference for the course is:
Le Veque -- Numerical Methods for Conservation Laws -- Birkhauser (1990 or 1992)
Alternatively, you may look at
LeVeque -- Finite Volume Methods for Hyperbolic Problems (2004)
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