"""
Initialize a smooth incompressible convergence test. Here, the
velocities are initialized as
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 is then
u(x,y,t) = 1 - 2 cos(2 pi (x - t)) sin(2 pi (y - t))
v(x,y,t) = 1 + 2 sin(2 pi (x - t)) cos(2 pi (y - t))
p(x,y,t) = -cos(4 pi (x - t)) - cos(4 pi (y - t))
The numerical solution can be compared to the exact solution to
measure the convergence rate of the algorithm.
"""
from __future__ import print_function
import math
import numpy as np
import mesh.patch as patch
from util import msg
[docs]def init_data(my_data, rp):
""" initialize the incompressible converge problem """
msg.bold("initializing the incompressible converge problem...")
# make sure that we are passed a valid patch object
if not isinstance(my_data, patch.CellCenterData2d):
print(my_data.__class__)
msg.fail("ERROR: patch invalid in converge.py")
# 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)
[docs]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_converge_error.py
"""
print(ostr)