#!/usr/bin/gnuplot

# compare sph/heatconduction output with analytic solution to diffusion equation

alpha = 1.0e-4
time = 4.0

analytic_profile(x) = 1.5 + 0.5*erf((x-49.5e-2)/sqrt(4.0*alpha*time))

set ylabel "internal energy per particle"
set xlabel "x position [m]"

plot [][0.5:2.5]'dump.last' u 3:6 ti "SPH simulation", analytic_profile(x) ti "analytic solution"

pause -1
#set terminal postscript color enhanced lw 2
#set out "heat_profile.ps"
set table "simu.dat"
plot [0:1][0.5:2.5]'dump.last' u 3:6

set table "analytic.dat"
set samples 1000
plot [0:1][0.5:2.5] analytic_profile(x)
#replot