"""The Gresho vortex problem sets up a toroidal velocity field that is
balanced by a radial pressure gradient.  This is in equilibrium and
the state should remain unchanged in time.  This version of the problem
is based on Miczek, Roepke, and Edelmann 2014."""

import numpy as np

from pyro.util import msg

DEFAULT_INPUTS = "inputs.gresho"

PROBLEM_PARAMS = {"gresho.rho0": 1.0,  # density in the domain
                  "gresho.r": 0.2,  # radial location of peak velocity
                  "gresho.mach": 0.1,  # Mach number
                  "gresho.t_r": 1.0}  # reference time (used for setting peak velocity)



[docs]
def init_data(my_data, rp):
    """ initialize the Gresho vortex problem """

    if rp.get_param("driver.verbose"):
        msg.bold("initializing the Gresho vortex problem...")

    # get the density and velocities
    dens = my_data.get_var("density")
    xmom = my_data.get_var("x-momentum")
    ymom = my_data.get_var("y-momentum")
    ener = my_data.get_var("energy")

    myg = my_data.grid

    x_center = 0.5 * (myg.x[0] + myg.x[-1])
    y_center = 0.5 * (myg.y[0] + myg.y[-1])
    L_x = myg.xmax - myg.xmin

    gamma = rp.get_param("eos.gamma")

    rho0 = rp.get_param("gresho.rho0")
    M = rp.get_param("gresho.mach")

    rr = rp.get_param("gresho.r")
    t_r = rp.get_param("gresho.t_r")

    q_r = 0.4 * np.pi * L_x / t_r

    # pressure peaks at r = rr, and has the value
    # p0 + 12.5 * rr**2
    #
    # Mach number is M = q |u_phi| / sqrt(gamma p / rho),
    #
    # so p0 is found as:
    #
    # p0 + 12.5 rr**2 = rho q**2 |u_phi|**2 / (gamma M**2)
    #
    # where u_phi peaks at 5 * rr

    p0 = rho0 * q_r**2 * (5 * rr)**2 / (gamma * M**2) - 12.5 * rr**2

    pres = myg.scratch_array()
    u_phi = myg.scratch_array()

    dens[:, :] = rho0
    pres[:, :] = p0

    rad = np.sqrt((myg.x2d - x_center)**2 +
                  (myg.y2d - y_center)**2)

    indx1 = rad < rr
    u_phi[indx1] = 5.0 * rad[indx1]
    pres[indx1] = p0 + 12.5 * rad[indx1]**2

    indx2 = np.logical_and(rad >= rr, rad < 2.0*rr)
    u_phi[indx2] = 2.0 - 5.0 * rad[indx2]
    pres[indx2] = p0 + 12.5 * rad[indx2]**2 + \
        4.0 * (1.0 - 5.0 * rad[indx2] - np.log(rr) + np.log(rad[indx2]))

    indx3 = rad >= 2.0 * rr
    u_phi[indx3] = 0.0
    pres[indx3] = p0 + 12.5 * (2.0 * rr)**2 + \
        4.0 * (1.0 - 5.0 * (2.0 * rr) - np.log(rr) + np.log(2.0 * rr))

    xmom[:, :] = -dens[:, :] * q_r * u_phi[:, :] * (myg.y2d - y_center) / rad[:, :]
    ymom[:, :] = dens[:, :] * q_r * u_phi[:, :] * (myg.x2d - x_center) / rad[:, :]

    ener[:, :] = pres[:, :] / (gamma - 1.0) + \
                0.5 * (xmom[:, :]**2 + ymom[:, :]**2) / dens[:, :]

    # report peak Mach number
    cs = np.sqrt(gamma * pres / dens)
    M = np.abs(q_r * u_phi).max() / cs.max()
    print(f"peak Mach number = {M}")




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