Source code for pyro.incompressible_viscous.problems.converge

r"""
Initialize a smooth incompressible+viscous convergence test.  Here, the
velocities are initialized as

.. math::

    u(x,y) = 1 - 2 \cos(2 \pi x) \sin(2 \pi y)

    v(x,y) = 1 + 2 \sin(2 \pi x) \cos(2 \pi y)

and the exact solution at some later time t, for some viscosity nu, is

.. math::

    u(x,y,t) = 1 - 2 \cos(2 \pi (x - t)) \sin(2 \pi (y - t)) e^{-8 \pi^2 \nu t}

    v(x,y,t) = 1 + 2 \sin(2 \pi (x - t)) \cos(2 \pi (y - t)) e^{-8 \pi^2 \nu t}

    p(x,y,t) = - (\cos(4 \pi (x - t)) + \cos(4 \pi (y - t))) e^{-16 \pi^2 \nu t}

The numerical solution can be compared to the exact solution to
measure the convergence rate of the algorithm.
"""


import math

import numpy as np

from pyro.util import msg

DEFAULT_INPUTS = "inputs.converge.64"

PROBLEM_PARAMS = {}




def init_data(my_data, rp):
    """ initialize the incompressible viscous converge problem """

    if rp.get_param("driver.verbose"):
        msg.bold("initializing the incompressible viscous converge problem...")

    # get the velocities
    u = my_data.get_var("x-velocity")
    v = my_data.get_var("y-velocity")

    myg = my_data.grid

    if (myg.xmin != 0 or myg.xmax != 1 or
        myg.ymin != 0 or myg.ymax != 1):
        msg.fail("ERROR: domain should be a unit square")

    u[:, :] = 1.0 - 2.0*np.cos(2.0*math.pi*myg.x2d)*np.sin(2.0*math.pi*myg.y2d)
    v[:, :] = 1.0 + 2.0*np.sin(2.0*math.pi*myg.x2d)*np.cos(2.0*math.pi*myg.y2d)





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

    ostr = """
          Comparisons to the analytic solution can be done using
          analysis/incomp_viscous_converge_error.py
          """

    print(ostr)