""" A simulation of diffusion """

import matplotlib.pyplot as plt
import numpy as np

from pyro.mesh import patch
from pyro.multigrid import MG
from pyro.simulation_null import NullSimulation, bc_setup, grid_setup
from pyro.util import msg



[docs]
class Simulation(NullSimulation):
    """ A simulation of diffusion """


[docs]
    def initialize(self):
        """
        Initialize the grid and variables for diffusion and set the initial
        conditions for the chosen problem.
        """

        # setup the grid
        my_grid = grid_setup(self.rp, ng=1)

        # for MG, we need to be a power of two
        if my_grid.nx != my_grid.ny:
            msg.fail("need nx = ny for diffusion problems")

        n = int(np.log(my_grid.nx)/np.log(2.0))
        if 2**n != my_grid.nx:
            msg.fail("grid needs to be a power of 2")

        # create the variables

        # first figure out the boundary conditions -- we allow periodic,
        # Dirichlet, and Neumann.

        bc, _, _ = bc_setup(self.rp)

        for bnd in [bc.xlb, bc.xrb, bc.ylb, bc.yrb]:
            if bnd not in ["periodic", "neumann", "dirichlet"]:
                msg.fail("invalid BC")

        my_data = patch.CellCenterData2d(my_grid)
        my_data.register_var("phi", bc)
        my_data.create()

        self.cc_data = my_data

        # now set the initial conditions for the problem
        self.problem_func(self.cc_data, self.rp)



[docs]
    def method_compute_timestep(self):
        """
        The diffusion timestep() function computes the timestep
        using the explicit timestep constraint as the starting point.
        We then multiply by the CFL number to get the timestep.
        Since we are doing an implicit discretization, we do not
        require CFL < 1.
        """

        cfl = self.rp.get_param("driver.cfl")
        k = self.rp.get_param("diffusion.k")

        # the timestep is min(dx**2/k, dy**2/k)
        xtmp = self.cc_data.grid.dx**2/k
        ytmp = self.cc_data.grid.dy**2/k

        self.dt = cfl*min(xtmp, ytmp)



[docs]
    def evolve(self):
        """
        Diffusion through dt using C-N implicit solve with multigrid
        """

        self.cc_data.fill_BC_all()
        phi = self.cc_data.get_var("phi")
        myg = self.cc_data.grid

        # diffusion coefficient
        k = self.rp.get_param("diffusion.k")

        # setup the MG object -- we want to solve a Helmholtz equation
        # equation of the form:
        # (alpha - beta L) phi = f
        #
        # with alpha = 1
        #      beta  = (dt/2) k
        #      f     = phi + (dt/2) k L phi
        #
        # this is the form that arises with a Crank-Nicolson discretization
        # of the diffusion equation.
        mg = MG.CellCenterMG2d(myg.nx, myg.ny,
                               xmin=myg.xmin, xmax=myg.xmax,
                               ymin=myg.ymin, ymax=myg.ymax,
                               xl_BC_type=self.cc_data.BCs['phi'].xlb,
                               xr_BC_type=self.cc_data.BCs['phi'].xrb,
                               yl_BC_type=self.cc_data.BCs['phi'].ylb,
                               yr_BC_type=self.cc_data.BCs['phi'].yrb,
                               alpha=1.0, beta=0.5*self.dt*k,
                               verbose=0)

        # form the RHS: f = phi + (dt/2) k L phi  (where L is the Laplacian)
        f = mg.soln_grid.scratch_array()
        f.v()[:, :] = phi.v() + 0.5*self.dt*k * (
            (phi.ip(1) + phi.ip(-1) - 2.0*phi.v())/myg.dx**2 +
            (phi.jp(1) + phi.jp(-1) - 2.0*phi.v())/myg.dy**2)

        mg.init_RHS(f)

        # initial guess is zeros
        mg.init_zeros()

        # solve the MG problem for the updated phi
        mg.solve(rtol=1.e-10)
        # mg.smooth(mg.nlevels-1,100)

        # update the solution
        phi.v()[:, :] = mg.get_solution().v()

        # increment the time
        self.cc_data.t += self.dt
        self.n += 1



[docs]
    def dovis(self):
        """
        Do runtime visualization.
        """

        plt.clf()

        phi = self.cc_data.get_var("phi")

        myg = self.cc_data.grid

        img = plt.imshow(np.transpose(phi.v()),
                   interpolation="nearest", origin="lower",
                   extent=[myg.xmin, myg.xmax, myg.ymin, myg.ymax],
                   cmap=self.cm)

        plt.xlabel("x")
        plt.ylabel("y")
        plt.title("phi")

        plt.colorbar(img)

        plt.figtext(0.05, 0.0125, f"t = {self.cc_data.t:10.5f}")

        plt.pause(0.001)
        plt.draw()