APPM 7400-003

HYPERBOLIC SYSTEMS
Spring 2001 Schedule

F  11:00-11:50, ECOT 226



Last Updated on 4/19/2001.
Date
Topics
Remarks
I. Waves and shocks in hyperbolic systems
F: January 19 Scalar linear advection equation - linear wave equation - characteristics and Riemann Invariants - classification of first order systems of PDEs
F: January 26 Scalar nonlinear equations - Burgers equation - shocks and Rankine-Hugoniot relations
F: February 2 Burgers equation - shocks and Rankine-Hugoniot relations - dissipation
F: February 9 Riemann problem - Nonlinear systems - isothermal Euler equations
F: February 16 Isothermal Euler equations: Riemann Invariants
F: February 23 The Euler equations of gas dynamics: waves and shocks
F: March 2 The Euler equations of gas dynamics - discussion Assignment I Assignment I (gzipped postscript)
Euler equations (mathematica notebook)
Euler equations (gzipped postscript)
II. Numerical schemes for flows with shocks
F: March 9 Finite difference schemes for the scalar linear advection equation in 1D
F: March 16 Second order accurate shock-capturing schemes - schemes for nonlinear equations
F: March 23 Schemes for systems Assignment I due 
F: March 30 Spring Break
F: April 6 Copper Mountain Multigrid Conference
III. Hyperbolic systems: advanced topics
F: April 13 no class
F: April 20 Finite Volume schemes in 1D, 2D, 3D Assignment II (gzipped postscript)
Article Shallow Water MHD (pdf)
shallow.f90
parameters.h (for shallow.f90)
laxmpi.f90
M: April 23 implementation of 2D Burgers equation on parallel computers using MPI
F: April 27 Derivation of MHD from Euler + Maxwell
F: May 4 Derivation of MHD from Euler + Maxwell - MHD waves Assignment II due
solution of assignment II:
matlab file
shock1.eps
shock2.eps
rarefaction1.eps
rarefaction2.eps
next year:     -steady Euler and MHD flows: elliptic and hyperbolic flow regions
    -compound shocks
    -overcompressive shocks
    -MHD bow shock flows with applications in Space Physics
    -time-dependent linear elasticity: waves and shocks
    -relativistic Euler and MHD: waves and shocks
    -waves in systems with dissipation
    -viscous profiles for shocks
    -entropy symmetrization of hyperbolic systems
    -space-time schemes
    -residual distribution finite element schemes for flows with shocks
    -MHD shocks
No Final Exam 

By Hans De Sterck
Email: desterck@colorado.edu