Please report all errors/typos. etc to Matt Choptuik at [email protected]
Last updated March 26, 2010
Lecture Notes
Week 1: Solution of Classical
Field Equations Using Finite Difference Techniques (MW Choptuik)
- Solving the wave equation using finite difference techniques [PDF]
- The 3+1 approach to the Einstein equations [PDF]
- Time dependent spherically symmetric (SS) spacetimes and the SS
Einstein-massless-Klein-Gordon system [PDF]
- Project 1 handout [PDF]
Week 2: Much Ado About Hydrodynamics
and Related Problems (L Lehner)
- Overview and Burger's equation (includes Project 2) [PDF]
- General Relativistic Hydrodynamics and beyond [PDF]
Week 3: Miscellaneous topics (F Pretorius)
- Lecture 1: Overview [PDF]
- Lecture 4: AMR [PDF]
Project 2:
Ultrarelativistic
Hydrodynamics
- Project handout (Secs. 5,6 and 7 of notes: begins at page 10) [PDF]
- Code for solution of Burger's equation. Distribution: burgers.tar.gz
- burgers_rnpl
- init_q.inc
- step.inc
- calc_A.f
- calc_eta.f
- calc_f.f
- calc_FF.f
- calc_flux.f
- calc_lambda.f
- calc_omega.f
- indep_res.f
- minmod.f
- norm.f
- recos_qL.f
- recos_qR.f'
- update_boundary.f
- update_q.f
- Code for exact solution of Burger's
equation. Distribution: burgers_exact.tar.gz
- Animations made with burgers_exact and burgers. Three
distinct initial data sets are used, two Riemann (shock tube)
configurations and one generic smooth initial data (Gaussian).
Specifically
- R1: Riemann problem 1: Shock: q_L=1.0 q_R=0.1
- Exact solution [MPEG]
- Exact solution & Roe solution [MPEG]
- R2: Riemann problem 2: Fan: q_L=0.1 q_R=1.0
- Exact solution [MPEG]
- Exact solution & Roe solution [MPEG]
- G: Gaussian initial profile
- Roe solution applied to q_t + (1/2 q^2)_x = 0 [MPEG]
- Roe solution & first-order upwind applied to q_t + q q_x
= 0 [MPEG]
- Roe solution & first-order upwind applied to q_t + (1/2
q^2)_x = 0 [MPEG]
- Roe solution & second-order upwind applied to q_t + (1/2
q^2)_x = 0 [MPEG]
- Code for exact solution of Riemann
problem for ultrarelativistic
fluid. Distribution: ultra_exact.tar.gz
- Animation made with ultra_exact and the current key for the
problem, ultra as implemented by Pretorius/Olabarietta
- R1: Riemann problem 1: Shock/Fan q_L=1.0 q_R=0.1:
Pressure [MPEG]
- HINTS for groups having
difficulties with the
implementation.
- Version of properly functioning code's step.inc
with numerous calls to dvdump (see below) added to provide a
detailed trace of top-level steps in the evolution algorithm. You
should try to instrument your implementation of step.inc with
identical calls to dvdump in order to easily compare your
results with ours.
- Initial data file id0
for an evolution consisting of a single time step (apart from the
initial time), on a mesh with 16 total grid cells, and for shock tube
data with rho_R = 0.1, rho_L = 1.0, v_R = v_L = 0.
Again, to compare with our results you will need to ensure that the
parameter file that you use matches this one in all relevant
respects.
- Output file fort.80
containing debugging trace from dvdump, using above parameter
file, and the functioning code.
- Source code for dvdump.f.
Download this file into your code directory, and, in the Makefile,
add dvdump.o to the list of object files on which the
executable depends. Ask an instructor if you have any questions
concerning this.
Project 3:
Teukolsky Equation