1D ADM gravitational wave simulation
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README
adm1d_v1.lua
adm1d_v2.lua
adm2dspherical.lua
adm2dspherical2.lua
adm3d.lua
boundary.lua
bssnok1d.lua
bssnok1d_backwardeuler_linear.lua
bssnok1d_backwardeuler_newton.lua
bssnok1d_original.lua
bssnok1d_original_backwardeuler_linear.lua
bssnok1d_original_fe.lua
bssnok3d.lua
emhd.lua
equation.lua
euler1d.lua
euler1d_backwardeuler_linear.lua
euler1d_backwardeuler_newton.lua
euler1d_burgers.lua
euler1d_dft.lua
euler1d_godunov.lua
euler1d_quasilinear.lua
euler1d_selfsimilar.lua
euler3d.lua
font.png
hll.lua
integrators.lua
limiter.lua
linearsolvers.lua
mat33.lua
mat33sym.lua
maxwell.lua
mhd.lua
muscl.lua
nls-sim.lua
plm-v2.lua
plm.lua
ppm.lua
roe.lua
roe_implicit_linearized.lua
roe_newton_krylov.lua
run.lua
sod_exact.lua
solver.lua
solverfv.lua
srhd1d.lua
srhd1d_roe.lua
weno5.lua
z4-1d-v2.lua
z4-1d.lua
z4-3d.lua

README

Numerical simulation of hyperbolic formalisms
Made for getting some numerical relativity demos working

Requires my lua-ext, symmath-lua, and optionally lua-glapp, and the Malkia UFO ffi lua files for the OpenGL display.
There's a text-based version you can uncomment that will run it to the command-line if you don't want to bother set up the GL stuff.

adm1d_v1.lua is based on formalism described in Alcubierre's "Introduction to 3+1 Numerical Relativity" in the Toy 1+1 example chapter.
Specifically, a 3-variable hyperbolic system with lapse (alpha) and metric (g) separated from the state variable computations.

adm1d5var.lua is a hyperbolic sim based on Alcubierre's "The appearance of coordinate shocks in hyperbolic formalisms of General Relativity"
found here: http://arxiv.org/pdf/gr-qc/9609015v2.pdf

adm2dspherical.lua is the spherical solution in the same paper mentioned above.
Figured out that the paper's, "eigenfields" is an inner product with the variable basis and the rows that make up the inverse eigenvector matrix.

adm3d.lua is my start on a 3D implementation according to the gauge shock paper.
Maybe I'll also use Alcubierre's "Introduction to Numerical Relativity" paper found here: http://cgwa.phys.utb.edu/Files/Events/29_610_Alcubierre_numerical.pdf

euler1d.lua is the Euler hydrodynamic equations I used as a test-case to verify the Roe solver was working.  Good ol' Euler fluid equations.

maxwell.lua is Maxwell equations described as hyperbolic equations in section 4.3 of Trangenstein's "Numerical Solutions of Hyperbolic Partial Differential Equations"

bssnok1d.lua is a hodge-podge of the BSSNOK partial wrt time and the hyperbolic formalism of BSSNOK described in Alcubierre's Hyperbolicity chapter.

mhd.lua is based on "ATHENA: A NEW CODE FOR ASTROPHYSICAL MHD" 2008 by Stone, Gardiner, Teuben, Hawley, and Simon

and then I started adding attempts at implicit solvers.
the backward-euler conj.res. implicit and the backward-euler newton+conj.res. implicit don't work so great at the moment.
the roe+backward-euler conj.res. implicit is stable for a while, but with some errors at boundary conditions (which probably what makes it explode... I hope)