"""Initialize the profile to a Gaussian.  With a constant
conductivity, an initial Gaussian profile remains Gaussian, with the
peak lowering and width increasing with time.  This allows this
problem to be used for verification.

"""

import numpy

from pyro.util import msg

DEFAULT_INPUTS = "inputs.gaussian"

PROBLEM_PARAMS = {"gaussian.t_0": 0.001,
                  "gaussian.phi_0": 1.0,
                  "gaussian.phi_max": 2.0}



[docs]
def phi_analytic(dist, t, t_0, k, phi_1, phi_2):
    """ the analytic solution to the Gaussian diffusion problem """
    phi = (phi_2 - phi_1)*(t_0/(t + t_0)) * \
        numpy.exp(-0.25*dist**2/(k*(t + t_0))) + phi_1
    return phi




[docs]
def init_data(my_data, rp):
    """ initialize the Gaussian diffusion problem """

    if rp.get_param("driver.verbose"):
        msg.bold("initializing the Gaussian diffusion problem...")

    phi = my_data.get_var("phi")

    xmin = my_data.grid.xmin
    xmax = my_data.grid.xmax

    ymin = my_data.grid.ymin
    ymax = my_data.grid.ymax

    xctr = 0.5*(xmin + xmax)
    yctr = 0.5*(ymin + ymax)

    k = rp.get_param("diffusion.k")
    t_0 = rp.get_param("gaussian.t_0")
    phi_max = rp.get_param("gaussian.phi_max")
    phi_0 = rp.get_param("gaussian.phi_0")

    dist = numpy.sqrt((my_data.grid.x2d - xctr)**2 +
                      (my_data.grid.y2d - yctr)**2)

    phi[:, :] = phi_analytic(dist, 0.0, t_0, k, phi_0, phi_max)

    # for later interpretation / analysis, store some auxiliary data
    my_data.set_aux("k", k)
    my_data.set_aux("t_0", t_0)
    my_data.set_aux("phi_0", phi_0)
    my_data.set_aux("phi_max", phi_max)




[docs]
def finalize():
    """ print out any information to the user at the end of the run """

    ostr = """
          The solution can be compared to the analytic solution with
          the script analysis/gauss_diffusion_compare.py
          """

    print(ostr)