APPM 7400, Section 003, Spring 2001

HYPERBOLIC SYSTEMS

COURSE NOTES HYPERBOLIC SYSTEMS (SPRING 2001)

The course notes as they were distributed in the lectures (pdf file, 2 slides per page).
(They cover most of the material that was discussed in the lectures, but not everything,
and sometimes in a different order).
These notes are based on the notes referred to below.

MY LECTURE NOTES of the course `Basic properties of nonlinear
magnetohydrodynamic flows: theory and simulations'

I gave this course at the Centre forPlasma Astrophysics of the Katholieke Universiteit Leuven, Belgium, in Spring 2000.
These notes cover much of the same material that I discuss in APPM7400-003, but the order may differ. Still these notes are good as reference material and for additional examples. I will use a slightly reworked version of the second part on numerical methods in APPM7400-003.

Part I: Introduction (with examples of astrophysical flows with shocks!)and general theory of hyperbolic conservation laws (scalar and system). [gzipped postscript]
Part II: Finite difference and finite volume schemes for numericalsimulation of flows with shocks. [gzipped postscript]
Part III: A classification of nonlinear wave mode types in hyperbolicsystems and a discussion of MHD discontinuities . [gzipped postscript]
Homework assignments. [gzipped postscript]

MY PhD THESIS `Numerical simulation and analysis of magneticallydominated MHD bow shock flows with applications in space physics'

You can find more background material for the course in my PhD thesis text, both on the basic theory and on more advanced applications in MHD and Space Physics bow shock simulations. Gzipped postscript files of the thesis chapters can be found here.

REFERENCE MATERIAL

Leveque, Numerical methods for conservation laws,Birkhauser, 1992. (introductory; analytical + numerical;scalar, Euler)

Kroener, Numerical schemes for conservation laws,Wiley, 1997. (advanced; analytical + numerical;scalar, Euler)

Hoffmann and Chiang, Computational Fluid Dynamics forEngineers (volumes I and II), Engineering Education System,1993. (introductory lecture notes; analytical + numerical;scalar, Euler)

Leveque, Nonlinear Conservation Laws and Finite Volume Methodsfor Astrophysical Fluid Flow, in Computational Methodsfor Astrophysical Fluid Flow, editedby O. Steiner andA. Gautschy, Springer-Verlag, 1998. (introductory lecturenotes; analytical + numerical; Euler, MHD, relativity) ftp://amath.washington.edu/pub/rjl/papers/saasfee.ps.gz

Courant and Hilbert, Methods of mathematical physics, vol. 2,Interscience, 1962. (advanced; analytical; Euler, MHD)

Courant and Friedrichs, Supersonic flow and shock waves,Interscience,1948. (advanced; analytical; Euler)

Whitham, Linear and nonlinear waves, Wiley-Interscience, 1974.(advanced; analytical; Euler, MHD)

Landau and Lifshitz, Electrodynamics of Continuous Media,Pergamon, 1984. (advanced; analytical; MHD)

Jeffrey and Taniuti, Nonlinear wave propagation, AcademicPress, 1964.(advanced; analytical; MHD)

Anderson, Magnetohydrodynamic shock waves, MIT Press, 1963.(advanced;analytical; MHD)

Hans De Sterck