Graduate Summer School on General Relativistic Hydrodynamics

Computational Lab Page

Please report all errors/typos. etc to Matt Choptuik at [email protected]

Last updated July 28, 2003.

On-line Material from the Lectures

Lab Groups

A preliminary list of lab group assignments can be found HERE

Instructions to Students

In preparation for the computational lab component of the school, we ask that prior to the start of the school that you

Look through the Background/Reference Material listed below
Download the Project 1 handout, work through the notes therein, and complete Problems 1a) through 1g).

If you have any questions about, or problems with this material, send e-mail to the lab instructors.

Background/Reference Material and Related Software

General Relativity: Students are expected to have had at least a first course in general relativity. A number of excellent texts are available for those who feel the need for a refresher, including:
- C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation, W.H. Freeman, San Francisco, 1973
- R.M. Wald, General Relativity, The University of Chicago Press, Chicago, 1984.
- R.A. D'Inverno Introducing Einstein's Relativity, Oxford University Press, Oxford, 1997.
- B.F. Schutz A First Course in General Relativity, Cambridge University Press, Cambridge, 1985.
Relativistic Hydrodynamics: The following references provide useful background for the second project (currently under construction).
- J.M. Marti and E. Mueller, Numerical Hydrodynamics in Special Relativity: http://www.livingreviews.org/lrr-1999-3/
- J. Font, Numerical Hydrodynamics in General Relativity: http://www.livingreviews.org/lrr-2000-2/
- R.J. Leveque, Numerical Methods for Conservation Laws", Birkhauser-Verlag, Basel, 1990.
Unix Notes: [HTML] [PDF] Recommended reading for those students with limited exposure to Unix.
Basic Finite Difference Techniques for Time Dependent PDEs [PDF]
RNPL: RNPL is a special purpose, high-level computer language designed to facilitate the rapid development of finite-difference (FD) codes for the solution of time dependent systems of partial differential equations. A chief design goal of the language was to free the user from the need to worry about the many "book keeping" details (such as memory management, parameter definition, input and output facilities etc.) that typically constitute a large fraction of a "written-from-scratch" FD code. RNPL also allows the user to specify the discrete equations of motion that define the FD system to be solved in a natural, operator-based fashion.
The RNPL compiler translates RNPL source into several Fortran (or C) files, which are then further compiled and linked to produce an executable. In some circumstances, it is awkward, or simply not possible, to achieve a desired functionality using pure RNPL---for such cases, a mechanism is provided that allows essentially arbitrary user written Fortran (or C) code to be "imported" into the RNPL-generated program.
You will use RNPL in each of the three lab projects described below, and in preparation for this, it is recommended that you peruse the following RNPL documentation before the summer school starts.
- Chapters 8 and 9 [PDF] of Robert Marsa's PhD dissertation [PDF]
- RNPL Reference Manual: [HTML] [PDF]
- RNPL User's Guide: [HTML] [PDF]
- "New" Features of RNPL [HTML] (Use as supplement to User's Guide and Reference Manual)
xvs: xvs is an Xforms/OpenGL-based visualization utility developed at UBC, based on previous work at UT Austin and Toronto/CITA. xvs is particularly suited for the analysis of the output from FD codes that solve time-dependent PDEs in one space dimension, and you should find it useful in completing Projects 1 and 2.
- xvs documentation
(Rough) installation instructions for RNPL/xvs/DV on Linux.
DV is also an Xforms/OpenGL-based visualization utility developed at UBC, and is particularly suited for the analysis of the output from FD codes that solve time-dependent PDEs in 2, 3 (and even 1!) space dimension, and you should find it useful in completing Projects 3a and/or 3b.
- DV documentation
- Generating MPEG animations using DV

Project 1: Scalar Wave Evolution on a Schwarzschild Background

PROJECT HANDOUT [PDF]
Solving a simple 1D wave equation with RNPL: It is recommended that you quickly work through these notes, and use the RNPL source file, w1dcn/w1dcn_rnpl as a template for your implementation.
Generic Makefile for RNPL applications: Makefile.rnpl
Source files for w1dcnm, an extension of w1dcn that illustrates the incorporation of external source into RNPL code:
- w1dcnm_rnpl
- mass.inc
- mass_init.inc
- Distribution: w1dcnm.tar.gz

Project 2: 1D Ultrarelativistic Fluid

PROJECT HANDOUT [PDF]
Code for solution of Burger's equation. Distribution: burgers.tar.gz
Code for exact solution of Burger's equation. Distribution: burgers_exact.tar.gz
Code for exact solution of Riemann problem for ultrarelativistic fluid. Distribution: ultra_exact.tar.gz
HINTS for groups having difficulties with the implementation.
1. 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.
2. 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.
3. Output file fort.80 containing debugging trace from dvdump, using above parameter file, and the functioning code.
4. 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 3a: Teukolsky Equation on a Kerr Background in Kerr-Schild Coordinates

PROJECT HANDOUT [PDF]
Code for solution of azimuthally separated wave equation in polar coordinates: wave2d_sph.tar.gz
Instructions on use of DV and xvs for extraction of QNFs from simulation results.

Project 3b: 2-D Ultrarelativistic Fluid

PROJECT HANDOUT [PDF]
MPEG animations showing solution for initial data described in Problem 3b) of handout.
- Pressure: P_KH.mpg
- V_x: v_x_KH.mpg
- V_y: v_y_KH.mpg
MPEG animations showing solution for initial data described in Problem 3c) of handout.
- Pressure: P_jets.mpg
- V_x: v_x_jets.mpg
- V_y v_y_jets.mpg

Using the vn.physics.ubc.ca cluster

We have set you up accounts on our local ``Beowulf'' cluster of Pentium III machines. For faster turn-around and in order to avoid overloading the lnx machines, you should use the cluster as much as possible to run your 2-D calculations.

Ask the lab instructors if you have any questions concerning the use of the cluster, or if you have encounter any problem with its use.