In [1]:

    

import arrayfire as af
import numpy as np
import pylab as pl

from bolt.lib.physical_system import physical_system
from bolt.lib.nonlinear.nonlinear_solver import nonlinear_solver
from bolt.lib.linear.linear_solver import linear_solver

import domain
import boundary_conditions
import params
import initialize

import bolt.src.nonrelativistic_boltzmann.advection_terms as advection_terms
import bolt.src.nonrelativistic_boltzmann.collision_operator as collision_operator
import bolt.src.nonrelativistic_boltzmann.moments as moments

%matplotlib inline

# Optimized plot parameters to make beautiful plots:
pl.rcParams['figure.figsize']  = 12, 7.5
pl.rcParams['figure.dpi']      = 300
pl.rcParams['image.cmap']      = 'jet'
pl.rcParams['lines.linewidth'] = 1.5
pl.rcParams['font.family']     = 'serif'
pl.rcParams['font.weight']     = 'bold'
pl.rcParams['font.size']       = 20
pl.rcParams['font.sans-serif'] = 'serif'
pl.rcParams['text.usetex']     = True
pl.rcParams['axes.linewidth']  = 1.5
pl.rcParams['axes.titlesize']  = 'medium'
pl.rcParams['axes.labelsize']  = 'medium'

pl.rcParams['xtick.major.size'] = 8
pl.rcParams['xtick.minor.size'] = 4
pl.rcParams['xtick.major.pad']  = 8
pl.rcParams['xtick.minor.pad']  = 8
pl.rcParams['xtick.color']      = 'k'
pl.rcParams['xtick.labelsize']  = 'medium'
pl.rcParams['xtick.direction']  = 'in'

pl.rcParams['ytick.major.size'] = 8
pl.rcParams['ytick.minor.size'] = 4
pl.rcParams['ytick.major.pad']  = 8
pl.rcParams['ytick.minor.pad']  = 8
pl.rcParams['ytick.color']      = 'k'
pl.rcParams['ytick.labelsize']  = 'medium'
pl.rcParams['ytick.direction']  = 'in'


    

In [10]:

    

# Time parameters:
t_final = 0.1
N       = 256

domain.N_q1 = int(N)
domain.N_p1 = int(N)

if (params.p_dim==2):
    domain.N_q2 = int(N)
    domain.N_p2 = int(N)

dt = 32*1e-3/N

# Defining the physical system to be solved:
system = physical_system(domain,
                         boundary_conditions,
                         params,
                         initialize,
                         advection_terms,
                         collision_operator.BGK,
                         moments
                        )

N_g_q = system.N_ghost_q

# Declaring a linear system object which will evolve the defined physical system:
nls = nonlinear_solver(system)
ls  = linear_solver(system)


    

In [11]:

    

time_array  = np.arange(dt, t_final + dt, dt)

rho_data_nls = np.zeros(time_array.size)
rho_data_ls  = np.zeros(time_array.size)

# Storing data at time t = 0:
n_nls           = nls.compute_moments('density')
rho_data_nls[0] = af.max(n_nls[:, :, N_g_q:-N_g_q, N_g_q:-N_g_q])

n_ls           = ls.compute_moments('density')
rho_data_ls[0] = af.max(n_ls) 

for time_index, t0 in enumerate(time_array):

    print('time_step = ', time_index, 'of ', time_array.size)
    nls.strang_timestep(dt)
    ls.RK4_timestep(dt)

    n_nls                     = nls.compute_moments('density')
    rho_data_nls[time_index]  = af.max(n_nls[:, :, N_g_q:-N_g_q, N_g_q:-N_g_q])
    
    n_ls                    = ls.compute_moments('density')
    rho_data_ls[time_index] = af.max(n_ls) 

nls.dump_distribution_function('dump_files/nlsf_' + str(N))
ls.dump_distribution_function('dump_files/lsf_' + str(N))


    

    




time_step =  0 of  800
time_step =  1 of  800
time_step =  2 of  800
time_step =  3 of  800
time_step =  4 of  800
time_step =  5 of  800
time_step =  6 of  800
time_step =  7 of  800
time_step =  8 of  800
time_step =  9 of  800
time_step =  10 of  800
time_step =  11 of  800
time_step =  12 of  800
time_step =  13 of  800
time_step =  14 of  800
time_step =  15 of  800
time_step =  16 of  800
time_step =  17 of  800
time_step =  18 of  800
time_step =  19 of  800
time_step =  20 of  800
time_step =  21 of  800
time_step =  22 of  800
time_step =  23 of  800
time_step =  24 of  800
time_step =  25 of  800
time_step =  26 of  800
time_step =  27 of  800
time_step =  28 of  800
time_step =  29 of  800
time_step =  30 of  800
time_step =  31 of  800
time_step =  32 of  800
time_step =  33 of  800
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time_step =  72 of  800
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time_step =  117 of  800
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time_step =  119 of  800
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time_step =  626 of  800
time_step =  627 of  800
time_step =  628 of  800
time_step =  629 of  800
time_step =  630 of  800
time_step =  631 of  800
time_step =  632 of  800
time_step =  633 of  800
time_step =  634 of  800
time_step =  635 of  800
time_step =  636 of  800
time_step =  637 of  800
time_step =  638 of  800
time_step =  639 of  800
time_step =  640 of  800
time_step =  641 of  800
time_step =  642 of  800
time_step =  643 of  800
time_step =  644 of  800
time_step =  645 of  800
time_step =  646 of  800
time_step =  647 of  800
time_step =  648 of  800
time_step =  649 of  800
time_step =  650 of  800
time_step =  651 of  800
time_step =  652 of  800
time_step =  653 of  800
time_step =  654 of  800
time_step =  655 of  800
time_step =  656 of  800
time_step =  657 of  800
time_step =  658 of  800
time_step =  659 of  800
time_step =  660 of  800
time_step =  661 of  800
time_step =  662 of  800
time_step =  663 of  800
time_step =  664 of  800
time_step =  665 of  800
time_step =  666 of  800
time_step =  667 of  800
time_step =  668 of  800
time_step =  669 of  800
time_step =  670 of  800
time_step =  671 of  800
time_step =  672 of  800
time_step =  673 of  800
time_step =  674 of  800
time_step =  675 of  800
time_step =  676 of  800
time_step =  677 of  800
time_step =  678 of  800
time_step =  679 of  800
time_step =  680 of  800
time_step =  681 of  800
time_step =  682 of  800
time_step =  683 of  800
time_step =  684 of  800
time_step =  685 of  800
time_step =  686 of  800
time_step =  687 of  800
time_step =  688 of  800
time_step =  689 of  800
time_step =  690 of  800
time_step =  691 of  800
time_step =  692 of  800
time_step =  693 of  800
time_step =  694 of  800
time_step =  695 of  800
time_step =  696 of  800
time_step =  697 of  800
time_step =  698 of  800
time_step =  699 of  800
time_step =  700 of  800
time_step =  701 of  800
time_step =  702 of  800
time_step =  703 of  800
time_step =  704 of  800
time_step =  705 of  800
time_step =  706 of  800
time_step =  707 of  800
time_step =  708 of  800
time_step =  709 of  800
time_step =  710 of  800
time_step =  711 of  800
time_step =  712 of  800
time_step =  713 of  800
time_step =  714 of  800
time_step =  715 of  800
time_step =  716 of  800
time_step =  717 of  800
time_step =  718 of  800
time_step =  719 of  800
time_step =  720 of  800
time_step =  721 of  800
time_step =  722 of  800
time_step =  723 of  800
time_step =  724 of  800
time_step =  725 of  800
time_step =  726 of  800
time_step =  727 of  800
time_step =  728 of  800
time_step =  729 of  800
time_step =  730 of  800
time_step =  731 of  800
time_step =  732 of  800
time_step =  733 of  800
time_step =  734 of  800
time_step =  735 of  800
time_step =  736 of  800
time_step =  737 of  800
time_step =  738 of  800
time_step =  739 of  800
time_step =  740 of  800
time_step =  741 of  800
time_step =  742 of  800
time_step =  743 of  800
time_step =  744 of  800
time_step =  745 of  800
time_step =  746 of  800
time_step =  747 of  800
time_step =  748 of  800
time_step =  749 of  800
time_step =  750 of  800
time_step =  751 of  800
time_step =  752 of  800
time_step =  753 of  800
time_step =  754 of  800
time_step =  755 of  800
time_step =  756 of  800
time_step =  757 of  800
time_step =  758 of  800
time_step =  759 of  800
time_step =  760 of  800
time_step =  761 of  800
time_step =  762 of  800
time_step =  763 of  800
time_step =  764 of  800
time_step =  765 of  800
time_step =  766 of  800
time_step =  767 of  800
time_step =  768 of  800
time_step =  769 of  800
time_step =  770 of  800
time_step =  771 of  800
time_step =  772 of  800
time_step =  773 of  800
time_step =  774 of  800
time_step =  775 of  800
time_step =  776 of  800
time_step =  777 of  800
time_step =  778 of  800
time_step =  779 of  800
time_step =  780 of  800
time_step =  781 of  800
time_step =  782 of  800
time_step =  783 of  800
time_step =  784 of  800
time_step =  785 of  800
time_step =  786 of  800
time_step =  787 of  800
time_step =  788 of  800
time_step =  789 of  800
time_step =  790 of  800
time_step =  791 of  800
time_step =  792 of  800
time_step =  793 of  800
time_step =  794 of  800
time_step =  795 of  800
time_step =  796 of  800
time_step =  797 of  800
time_step =  798 of  800
time_step =  799 of  800

In [12]:

    

import h5py

# Checking the errors
def check_convergence():
    N     = np.array([32, 64, 128, 256])
    error = np.zeros(N.size)
    
    for i in range(N.size):

        print("N = ", i)
        h5f   = h5py.File('dump_files/nlsf_' + str(N[i]) + '.h5')
        nls_f = h5f['distribution_function'][:]
        h5f.close()    

        h5f  = h5py.File('dump_files/lsf_' + str(N[i]) + '.h5')
        ls_f = h5f['distribution_function'][:]
        h5f.close()

        error[i] = np.mean(abs(nls_f - ls_f))

    print(error)
    poly = np.polyfit(np.log10(N), np.log10(error), 1)
    print(poly)

    pl.loglog(N, error, 'o-', label = 'Numerical')
    pl.loglog(N, error[0]*32**2/N**2, '--', color = 'black', 
              label = r'$O(N^{-2})$'
             )
    pl.legend(loc = 'best')
    pl.ylabel('Error')
    pl.xlabel('$N$')


    

In [13]:

    

check_convergence()


    

    




N =  0
N =  1
N =  2
N =  3
[  2.27942488e-08   3.30019343e-09   7.41818882e-10   1.85096470e-10]
[-2.29861577 -4.2487949 ]