def doit():
myg = mesh.patch.Grid2d(4, 4, ng=2, xmax=1.0, ymax=1.0)
mydata = mesh.patch.CellCenterData2d(myg, dtype=np.int)
bco = bnd.BC(xlb="outflow", xrb="outflow",
ylb="outflow", yrb="outflow")
mydata.register_var("outflow", bco)
bcp = bnd.BC(xlb="periodic", xrb="periodic",
ylb="periodic", yrb="periodic")
mydata.register_var("periodic", bcp)
bcre = bnd.BC(xlb="reflect-even", xrb="reflect-even",
ylb="reflect-even", yrb="reflect-even")
mydata.register_var("reflect-even", bcre)
bcro = bnd.BC(xlb="reflect-odd", xrb="reflect-odd",
ylb="reflect-odd", yrb="reflect-odd")
mydata.register_var("reflect-odd", bcro)
mydata.create()
a = mydata.get_var("outflow")
for i in range(myg.ilo, myg.ihi+1):
for j in range(myg.jlo, myg.jhi+1):
a[i,j] = (i-myg.ilo) + 10*(j-myg.jlo) + 1
b = mydata.get_var("periodic")
c = mydata.get_var("reflect-even")
d = mydata.get_var("reflect-odd")
b[:,:] = a[:,:]
c[:,:] = a[:,:]
d[:,:] = a[:,:]
mydata.fill_BC("outflow")
mydata.fill_BC("periodic")
mydata.fill_BC("reflect-even")
mydata.fill_BC("reflect-odd")
print("outflow")
mydata.pretty_print("outflow")
print(" ")
print("periodic")
mydata.pretty_print("periodic")
print(" ")
print("reflect-even")
mydata.pretty_print("reflect-even")
print(" ")
print("reflect-odd")
mydata.pretty_print("reflect-odd")
def bc_setup(rp):
# first figure out the BCs
xlb_type = rp.get_param("mesh.xlboundary")
xrb_type = rp.get_param("mesh.xrboundary")
ylb_type = rp.get_param("mesh.ylboundary")
yrb_type = rp.get_param("mesh.yrboundary")
bc = bnd.BC(xlb=xlb_type, xrb=xrb_type, ylb=ylb_type, yrb=yrb_type)
# if we are reflecting, we need odd reflection in the normal
# directions for the velocity
bc_xodd = bnd.BC(xlb=xlb_type,
xrb=xrb_type,
ylb=ylb_type,
yrb=yrb_type,
odd_reflect_dir="x")
bc_yodd = bnd.BC(xlb=xlb_type,
xrb=xrb_type,
ylb=ylb_type,
yrb=yrb_type,
odd_reflect_dir="y")
return bc, bc_xodd, bc_yodd
def test_bcs_1d():
myg = patch.Grid1d(4, ng=2, xmax=1.0)
myd = patch.CellCenterData1d(myg, dtype=np.int)
bco = bnd.BC(xlb="outflow", xrb="outflow")
myd.register_var("outflow", bco)
bcp = bnd.BC(xlb="periodic", xrb="periodic")
myd.register_var("periodic", bcp)
bcre = bnd.BC(xlb="reflect-even", xrb="reflect-even")
myd.register_var("reflect-even", bcre)
bcro = bnd.BC(xlb="reflect-odd", xrb="reflect-odd")
myd.register_var("reflect-odd", bcro)
myd.create()
a = myd.get_var("outflow")
a.v()[:] = np.array([1, 2, 3, 4], dtype=int)
b = myd.get_var("periodic")
c = myd.get_var("reflect-even")
d = myd.get_var("reflect-odd")
b[:] = a[:]
c[:] = a[:]
d[:] = a[:]
myd.fill_BC("outflow")
# left ghost
assert a[myg.ilo - 1] == 1
# right ghost
assert a[myg.ihi + 1] == 4
myd.fill_BC("periodic")
# x-boundaries
assert b[myg.ilo - 1] == b[myg.ihi]
assert b[myg.ilo] == b[myg.ihi + 1]
myd.fill_BC("reflect-even")
# left -- we'll check 2 ghost cells here
# left
assert_array_equal(c[myg.ilo:myg.ilo + 2], c[myg.ilo - 2:myg.ilo][::-1])
# right
assert_array_equal(c[myg.ihi - 1:myg.ihi + 1],
c[myg.ihi + 1:myg.ihi + 3][::-1])
myd.fill_BC("reflect-odd")
# left -- we'll check 2 ghost cells here
# left
assert_array_equal(d[myg.ilo:myg.ilo + 2],
-1.0 * d[myg.ilo - 2:myg.ilo][::-1])
# right
assert_array_equal(d[myg.ihi - 1:myg.ihi + 1],
-1.0 * d[myg.ihi + 1:myg.ihi + 3][::-1])
def do_demo():
""" show examples of the patch methods / classes """
import util.io as io
# illustrate basic mesh operations
myg = Grid2d(8, 16, xmax=1.0, ymax=2.0)
mydata = CellCenterData2d(myg)
bc = bnd.BC()
mydata.register_var("a", bc)
mydata.create()
a = mydata.get_var("a")
a[:, :] = np.exp(-(myg.x2d - 0.5)**2 - (myg.y2d - 1.0)**2)
print(mydata)
# output
print("writing\n")
mydata.write("mesh_test")
print("reading\n")
myd2 = io.read("mesh_test")
print(myd2)
mydata.pretty_print("a")
def do_demo():
# illustrate basic mesh operations
myg = Grid2d(8, 16, xmax=1.0, ymax=2.0)
mydata = CellCenterData2d(myg)
bc = bnd.BC()
mydata.register_var("a", bc)
mydata.create()
a = mydata.get_var("a")
a[:,:] = np.exp(-(myg.x2d - 0.5)**2 - (myg.y2d - 1.0)**2)
print(mydata)
# output
print("writing\n")
mydata.write("mesh_test")
print("reading\n")
_, myd2 = read("mesh_test")
print(myd2)
mydata.pretty_print("a")
def bc_setup(rp):
# first figure out the BCs
try:
xlb_type = rp.get_param("mesh.xlboundary")
except KeyError:
xlb_type = "periodic"
msg.warning("mesh.xlboundary is not set, defaulting to periodic")
try:
xrb_type = rp.get_param("mesh.xrboundary")
except KeyError:
xrb_type = "periodic"
msg.warning("mesh.xrboundary is not set, defaulting to periodic")
try:
ylb_type = rp.get_param("mesh.ylboundary")
except KeyError:
ylb_type = "periodic"
msg.warning("mesh.ylboundary is not set, defaulting to periodic")
try:
yrb_type = rp.get_param("mesh.yrboundary")
except KeyError:
yrb_type = "periodic"
msg.warning("mesh.yrboundary is not set, defaulting to periodic")
bc = bnd.BC(xlb=xlb_type, xrb=xrb_type, ylb=ylb_type, yrb=yrb_type)
# if we are reflecting, we need odd reflection in the normal
# directions for the velocity
bc_xodd = bnd.BC(xlb=xlb_type,
xrb=xrb_type,
ylb=ylb_type,
yrb=yrb_type,
odd_reflect_dir="x")
bc_yodd = bnd.BC(xlb=xlb_type,
xrb=xrb_type,
ylb=ylb_type,
yrb=yrb_type,
odd_reflect_dir="y")
return bc, bc_xodd, bc_yodd
def doit():
# create our base grid and initialize it with sequential data
myg = patch.Grid2d(4, 8, ng=1)
myd = patch.CellCenterData2d(myg)
bc = bnd.BC()
myd.register_var("a", bc)
myd.create()
a = myd.get_var("a")
a[myg.ilo:myg.ihi + 1,
myg.jlo:myg.jhi + 1].flat = np.arange(myg.nx * myg.ny)
print("restriction test")
print("original (fine) array")
myd.pretty_print("a")
# create a coarse grid and fill the variable in it with restricted data
print(" ")
print("restricted array")
cg = patch.Grid2d(2, 4, ng=1)
cd = patch.CellCenterData2d(cg)
cd.register_var("a", bc)
cd.create()
a_coarse = cd.get_var("a")
a_coarse[:, :] = myd.restrict("a")[:, :]
cd.pretty_print("a")
print(" ")
print("prolongation test")
print("original (coarse) array w/ ghost cells")
a_coarse[:, :].flat = np.arange(cg.qx * cg.qy)
cd.pretty_print("a")
# create a new fine (base) grid and fill the variable in it prolonged data
# from the coarsened grid
print(" ")
print("prolonged array")
fg = patch.Grid2d(4, 8, ng=1)
fd = patch.CellCenterData2d(fg)
fd.register_var("a", bc)
fd.create()
a_fine = fd.get_var("a")
a_fine[:, :] = cd.prolong("a")[:, :]
fd.pretty_print("a")
def setup_method(self):
""" this is run before each test """
nx = 8
ny = 8
self.g = patch.Grid2d(nx, ny, ng=2, xmax=1.0, ymax=1.0)
self.d = patch.CellCenterData2d(self.g, dtype=np.int)
bco = bnd.BC(xlb="outflow",
xrb="outflow",
ylb="outflow",
yrb="outflow")
self.d.register_var("a", bco)
self.d.register_var("b", bco)
self.d.create()
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(math.log(my_grid.nx) / math.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.
xlb_type = self.rp.get_param("mesh.xlboundary")
xrb_type = self.rp.get_param("mesh.xrboundary")
ylb_type = self.rp.get_param("mesh.ylboundary")
yrb_type = self.rp.get_param("mesh.yrboundary")
bcparam = []
for bc in [xlb_type, xrb_type, ylb_type, yrb_type]:
if bc == "periodic": bcparam.append("periodic")
elif bc == "neumann": bcparam.append("neumann")
elif bc == "dirichlet": bcparam.append("dirichlet")
else:
msg.fail("invalid BC")
bc = bnd.BC(xlb=bcparam[0],
xrb=bcparam[1],
ylb=bcparam[2],
yrb=bcparam[3])
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
problem = importlib.import_module("diffusion.problems.{}".format(
self.problem_name))
problem.init_data(self.cc_data, self.rp)
def setup_method(self):
""" this is run before each test """
self.rp = runparams.RuntimeParameters()
self.rp.params["driver.tmax"] = 1.0
self.rp.params["driver.max_steps"] = 100
self.rp.params["driver.init_tstep_factor"] = 0.5
self.rp.params["driver.max_dt_change"] = 1.2
self.rp.params["driver.fix_dt"] = -1.0
self.sim = sn.NullSimulation("test", "test", self.rp)
myg = patch.Grid2d(8, 16)
myd = patch.CellCenterData2d(myg)
bc = bnd.BC()
myd.register_var("a", bc)
myd.create()
self.sim.cc_data = myd
def test_write_read():
myg = patch.Grid2d(8, 6, ng=2, xmax=1.0, ymax=1.0)
myd = patch.CellCenterData2d(myg)
bco = bnd.BC(xlb="outflow", xrb="outflow", ylb="outflow", yrb="outflow")
myd.register_var("a", bco)
myd.create()
a = myd.get_var("a")
a.v()[:, :] = np.arange(48).reshape(8, 6)
myd.write("io_test")
# now read it in
nd = io.read("io_test")
anew = nd.get_var("a")
assert_array_equal(anew.v(), a.v())
def read(filename):
"""read an HDF5 file and recreate the simulation object that holds the
data and state of the simulation.
"""
if not filename.endswith(".h5"):
filename += ".h5"
with h5py.File(filename, "r") as f:
# read the simulation information -- this only exists if the
# file was created as a simulation object
try:
solver_name = f.attrs["solver"]
problem_name = f.attrs["problem"]
t = f.attrs["time"]
n = f.attrs["nsteps"]
except KeyError:
# this was just a patch written out
solver_name = None
# read in the grid info and create our grid
grid = f["grid"].attrs
myg = patch.Grid2d(grid["nx"],
grid["ny"],
ng=grid["ng"],
xmin=grid["xmin"],
xmax=grid["xmax"],
ymin=grid["ymin"],
ymax=grid["ymax"])
# sometimes problems define custom BCs -- at the moment, we
# are going to assume that these always map to BC.user. We
# need to read these in now, since the variable creation
# requires it.
custom_bcs = read_bcs(f)
if custom_bcs is not None:
if solver_name in [
"compressible_fv4", "compressible_rk", "compressible_sdc"
]:
bc_solver = "compressible"
else:
bc_solver = solver_name
bcmod = importlib.import_module("{}.{}".format(bc_solver, "BC"))
for name in custom_bcs:
bnd.define_bc(name, bcmod.user, is_solid=custom_bcs[name])
# read in the variable info -- start by getting the names
gs = f["state"]
names = []
for n in gs:
names.append(n)
# create the CellCenterData2d object
myd = patch.CellCenterData2d(myg)
for n in names:
grp = gs[n]
bc = bnd.BC(xlb=grp.attrs["xlb"],
xrb=grp.attrs["xrb"],
ylb=grp.attrs["ylb"],
yrb=grp.attrs["yrb"])
myd.register_var(n, bc)
myd.create()
# auxillary data
for k in f["aux"].attrs:
myd.set_aux(k, f["aux"].attrs[k])
# restore the variable data
for n in names:
grp = gs[n]
data = grp["data"]
v = myd.get_var(n)
v.v()[:, :] = data[:, :]
# restore the particle data
try:
gparticles = f["particles"]
particle_data = gparticles["particle_positions"]
init_data = gparticles["init_particle_positions"]
my_particles = particles.Particles(myd, None, len(particle_data),
"array", particle_data,
init_data)
except KeyError:
my_particles = None
if solver_name is not None:
solver = importlib.import_module(solver_name)
sim = solver.Simulation(solver_name, problem_name, None)
sim.n = n
sim.cc_data = myd
sim.cc_data.t = t
sim.particles = my_particles
sim.read_extras(f)
if solver_name is not None:
return sim
return myd
def initialize(self):
"""
Initialize the grid and variables for incompressible flow and
set the initial conditions for the chosen problem.
"""
# setup the grid
nx = self.rp.get_param("mesh.nx")
ny = self.rp.get_param("mesh.ny")
xmin = self.rp.get_param("mesh.xmin")
xmax = self.rp.get_param("mesh.xmax")
ymin = self.rp.get_param("mesh.ymin")
ymax = self.rp.get_param("mesh.ymax")
my_grid = patch.Grid2d(nx, ny,
xmin=xmin, xmax=xmax,
ymin=ymin, ymax=ymax, ng=4)
# create the variables
# first figure out the BCs
xlb_type = self.rp.get_param("mesh.xlboundary")
xrb_type = self.rp.get_param("mesh.xrboundary")
ylb_type = self.rp.get_param("mesh.ylboundary")
yrb_type = self.rp.get_param("mesh.yrboundary")
bc = bnd.BC(xlb=xlb_type, xrb=xrb_type,
ylb=ylb_type, yrb=yrb_type)
# if we are reflecting, we need odd reflection in the normal
# directions for the velocity
bc_xodd = bnd.BC(xlb=xlb_type, xrb=xrb_type,
ylb=ylb_type, yrb=yrb_type,
odd_reflect_dir="x")
bc_yodd = bnd.BC(xlb=xlb_type, xrb=xrb_type,
ylb=ylb_type, yrb=yrb_type,
odd_reflect_dir="y")
my_data = patch.CellCenterData2d(my_grid)
# velocities
my_data.register_var("x-velocity", bc_xodd)
my_data.register_var("y-velocity", bc_yodd)
# density
my_data.register_var("density", bc)
# phi -- used for the projections
my_data.register_var("phi-MAC", bc)
my_data.register_var("phi", bc)
# gradp -- used in the projection and interface states. The BCs here
# are tricky. If we are periodic, then it is periodic. Otherwise,
# we just want to do first-order extrapolation (homogeneous Neumann)
my_data.register_var("gradp_x", bc)
my_data.register_var("gradp_y", bc)
my_data.create()
self.cc_data = my_data
# now set the initial conditions for the problem
problem = importlib.import_module("lm_combustion.problems.{}".format(self.problem_name))
problem.init_data(self.cc_data, self.rp)
def test_vc_constant(N):
# test the multigrid solver
nx = N
ny = nx
# create the coefficient variable -- note we don't want Dirichlet here,
# because that will try to make alpha = 0 on the interface. alpha can
# have different BCs than phi
g = patch.Grid2d(nx, ny, ng=1)
d = patch.CellCenterData2d(g)
bc_c = bnd.BC(xlb="neumann", xrb="neumann", ylb="neumann", yrb="neumann")
d.register_var("c", bc_c)
d.create()
c = d.get_var("c")
c[:, :] = alpha(g.x2d, g.y2d)
plt.clf()
plt.figure(num=1, figsize=(5.0, 5.0), dpi=100, facecolor='w')
plt.imshow(np.transpose(c[g.ilo:g.ihi + 1, g.jlo:g.jhi + 1]),
interpolation="nearest",
origin="lower",
extent=[g.xmin, g.xmax, g.ymin, g.ymax])
plt.xlabel("x")
plt.ylabel("y")
plt.title("nx = {}".format(nx))
plt.colorbar()
plt.savefig("mg_alpha.png")
# check whether the RHS sums to zero (necessary for periodic data)
rhs = f(g.x2d, g.y2d)
print("rhs sum: {}".format(np.sum(rhs[g.ilo:g.ihi + 1, g.jlo:g.jhi + 1])))
# create the multigrid object
a = MG.VarCoeffCCMG2d(nx,
ny,
xl_BC_type="dirichlet",
yl_BC_type="dirichlet",
xr_BC_type="dirichlet",
yr_BC_type="dirichlet",
coeffs=c,
coeffs_bc=bc_c,
verbose=1)
# initialize the solution to 0
a.init_zeros()
# initialize the RHS using the function f
rhs = f(a.x2d, a.y2d)
a.init_RHS(rhs)
# solve to a relative tolerance of 1.e-11
a.solve(rtol=1.e-11)
# alternately, we can just use smoothing by uncommenting the following
#a.smooth(a.nlevels-1,50000)
# get the solution
v = a.get_solution()
# compute the error from the analytic solution
b = true(a.x2d, a.y2d)
e = v - b
print(
" L2 error from true solution = %g\n rel. err from previous cycle = %g\n num. cycles = %d"
% (a.soln_grid.norm(e), a.relative_error, a.num_cycles))
# plot it
plt.clf()
plt.figure(num=1, figsize=(10.0, 5.0), dpi=100, facecolor='w')
plt.subplot(121)
plt.imshow(np.transpose(v[a.ilo:a.ihi + 1, a.jlo:a.jhi + 1]),
interpolation="nearest",
origin="lower",
extent=[a.xmin, a.xmax, a.ymin, a.ymax])
plt.xlabel("x")
plt.ylabel("y")
plt.title("nx = {}".format(nx))
plt.colorbar()
plt.subplot(122)
plt.imshow(np.transpose(e[a.ilo:a.ihi + 1, a.jlo:a.jhi + 1]),
interpolation="nearest",
origin="lower",
extent=[a.xmin, a.xmax, a.ymin, a.ymax])
plt.xlabel("x")
plt.ylabel("y")
plt.title("error")
plt.colorbar()
plt.tight_layout()
plt.savefig("mg_test.png")
# store the output for later comparison
my_data = a.get_solution_object()
my_data.write("mg_test")
def initialize(self):
"""
Initialize the grid and variables for low Mach atmospheric flow
and set the initial conditions for the chosen problem.
"""
myg = grid_setup(self.rp, ng=4)
bc_dens, bc_xodd, bc_yodd = bc_setup(self.rp)
my_data = patch.CellCenterData2d(myg)
my_data.register_var("density", bc_dens)
my_data.register_var("x-velocity", bc_xodd)
my_data.register_var("y-velocity", bc_yodd)
# we'll keep the internal energy around just as a diagnostic
my_data.register_var("eint", bc_dens)
# phi -- used for the projections. The boundary conditions
# here depend on velocity. At a wall or inflow, we already
# have the velocity we want on the boundary, so we want
# Neumann (dphi/dn = 0). For outflow, we want Dirichlet (phi
# = 0) -- this ensures that we do not introduce any tangental
# acceleration.
bcs = []
for bc in [
self.rp.get_param("mesh.xlboundary"),
self.rp.get_param("mesh.xrboundary"),
self.rp.get_param("mesh.ylboundary"),
self.rp.get_param("mesh.yrboundary")
]:
if bc == "periodic":
bctype = "periodic"
elif bc in ["reflect", "slipwall"]:
bctype = "neumann"
elif bc in ["outflow"]:
bctype = "dirichlet"
bcs.append(bctype)
bc_phi = bnd.BC(xlb=bcs[0], xrb=bcs[1], ylb=bcs[2], yrb=bcs[3])
my_data.register_var("phi-MAC", bc_phi)
my_data.register_var("phi", bc_phi)
# gradp -- used in the projection and interface states. We'll do the
# same BCs as density
my_data.register_var("gradp_x", bc_dens)
my_data.register_var("gradp_y", bc_dens)
my_data.create()
self.cc_data = my_data
# some auxillary data that we'll need to fill GC in, but isn't
# really part of the main solution
aux_data = patch.CellCenterData2d(myg)
aux_data.register_var("coeff", bc_dens)
aux_data.register_var("source_y", bc_yodd)
aux_data.create()
self.aux_data = aux_data
# we also need storage for the 1-d base state -- we'll store this
# in the main class directly.
self.base["rho0"] = Basestate(myg.ny, ng=myg.ng)
self.base["p0"] = Basestate(myg.ny, ng=myg.ng)
# now set the initial conditions for the problem
problem = importlib.import_module("lm_atm.problems.{}".format(
self.problem_name))
problem.init_data(self.cc_data, self.base, self.rp)
# Construct beta_0
gamma = self.rp.get_param("eos.gamma")
self.base["beta0"] = Basestate(myg.ny, ng=myg.ng)
self.base["beta0"].d[:] = self.base["p0"].d**(1.0 / gamma)
# we'll also need beta_0 on vertical edges -- on the domain edges,
# just do piecewise constant
self.base["beta0-edges"] = Basestate(myg.ny, ng=myg.ng)
self.base["beta0-edges"].jp(1)[:] = \
0.5*(self.base["beta0"].v() + self.base["beta0"].jp(1))
self.base["beta0-edges"].d[myg.jlo] = self.base["beta0"].d[myg.jlo]
self.base["beta0-edges"].d[myg.jhi + 1] = self.base["beta0"].d[myg.jhi]
def test_bcs():
myg = patch.Grid2d(4, 4, ng=2, xmax=1.0, ymax=1.0)
myd = patch.CellCenterData2d(myg, dtype=np.int)
bco = bnd.BC(xlb="outflow", xrb="outflow", ylb="outflow", yrb="outflow")
myd.register_var("outflow", bco)
bcp = bnd.BC(xlb="periodic",
xrb="periodic",
ylb="periodic",
yrb="periodic")
myd.register_var("periodic", bcp)
bcre = bnd.BC(xlb="reflect-even",
xrb="reflect-even",
ylb="reflect-even",
yrb="reflect-even")
myd.register_var("reflect-even", bcre)
bcro = bnd.BC(xlb="reflect-odd",
xrb="reflect-odd",
ylb="reflect-odd",
yrb="reflect-odd")
myd.register_var("reflect-odd", bcro)
myd.create()
a = myd.get_var("outflow")
a.v()[:, :] = np.fromfunction(lambda i, j: i + 10 * j + 1, (4, 4),
dtype=int)
b = myd.get_var("periodic")
c = myd.get_var("reflect-even")
d = myd.get_var("reflect-odd")
b[:, :] = a[:, :]
c[:, :] = a[:, :]
d[:, :] = a[:, :]
myd.fill_BC("outflow")
# left ghost
assert_array_equal(a[myg.ilo - 1, myg.jlo:myg.jhi + 1],
np.array([1, 11, 21, 31]))
# right ghost
assert_array_equal(a[myg.ihi + 1, myg.jlo:myg.jhi + 1],
np.array([4, 14, 24, 34]))
# bottom ghost
assert_array_equal(a[myg.ilo:myg.ihi + 1, myg.jlo - 1],
np.array([1, 2, 3, 4]))
# top ghost
assert_array_equal(a[myg.ilo:myg.ihi + 1, myg.jhi + 1],
np.array([31, 32, 33, 34]))
myd.fill_BC("periodic")
# x-boundaries
assert_array_equal(b[myg.ilo - 1, myg.jlo:myg.jhi + 1],
b[myg.ihi, myg.jlo:myg.jhi + 1])
assert_array_equal(b[myg.ilo, myg.jlo:myg.jhi + 1], b[myg.ihi + 1,
myg.jlo:myg.jhi + 1])
# y-boundaries
assert_array_equal(b[myg.ilo:myg.ihi + 1, myg.jlo - 1],
b[myg.ilo:myg.ihi + 1, myg.jhi])
assert_array_equal(b[myg.ilo:myg.ihi + 1, myg.jlo], b[myg.ilo:myg.ihi + 1,
myg.jhi + 1])
myd.fill_BC("reflect-even")
# left -- we'll check 2 ghost cells here -- now we use flipud here
# because our 'x' is the row index
# left
assert_array_equal(c[myg.ilo:myg.ilo + 2, myg.jlo:myg.ihi + 1],
np.flipud(c[myg.ilo - 2:myg.ilo, myg.jlo:myg.jhi + 1]))
# right
assert_array_equal(
c[myg.ihi - 1:myg.ihi + 1, myg.jlo:myg.jhi + 1],
np.flipud(c[myg.ihi + 1:myg.ihi + 3, myg.jlo:myg.jhi + 1]))
# bottom
assert_array_equal(c[myg.ilo:myg.ihi + 1, myg.jlo:myg.jlo + 2],
np.fliplr(c[myg.ilo:myg.ihi + 1, myg.jlo - 2:myg.jlo]))
# top
assert_array_equal(
c[myg.ilo:myg.ihi + 1, myg.jhi - 1:myg.jhi + 1],
np.fliplr(c[myg.ilo:myg.ihi + 1, myg.jhi + 1:myg.jhi + 3]))
myd.fill_BC("reflect-odd")
# left -- we'll check 2 ghost cells here -- now we use flipud here
# because our 'x' is the row index
# left
assert_array_equal(d[myg.ilo:myg.ilo + 2, myg.jlo:myg.ihi + 1],
-np.flipud(d[myg.ilo - 2:myg.ilo, myg.jlo:myg.jhi + 1]))
# right
assert_array_equal(
d[myg.ihi - 1:myg.ihi + 1, myg.jlo:myg.jhi + 1],
-np.flipud(d[myg.ihi + 1:myg.ihi + 3, myg.jlo:myg.jhi + 1]))
# bottom
assert_array_equal(d[myg.ilo:myg.ihi + 1, myg.jlo:myg.jlo + 2],
-np.fliplr(d[myg.ilo:myg.ihi + 1, myg.jlo - 2:myg.jlo]))
# top
assert_array_equal(
d[myg.ilo:myg.ihi + 1, myg.jhi - 1:myg.jhi + 1],
-np.fliplr(d[myg.ilo:myg.ihi + 1, myg.jhi + 1:myg.jhi + 3]))
# test the boundary fill routine
from __future__ import print_function
import numpy as np
import mesh.patch
import mesh.boundary as bnd
myg = mesh.patch.Grid2d(4, 4, ng=2, xmax=1.0, ymax=1.0)
mydata = mesh.patch.CellCenterData2d(myg, dtype=np.int)
bco = bnd.BC(xlb="outflow", xrb="outflow", ylb="outflow", yrb="outflow")
mydata.register_var("outflow", bco)
bcp = bnd.BC(xlb="periodic", xrb="periodic", ylb="periodic", yrb="periodic")
mydata.register_var("periodic", bcp)
bcre = bnd.BC(xlb="reflect-even",
xrb="reflect-even",
ylb="reflect-even",
yrb="reflect-even")
mydata.register_var("reflect-even", bcre)
bcro = bnd.BC(xlb="reflect-odd",
xrb="reflect-odd",
ylb="reflect-odd",
yrb="reflect-odd")
mydata.register_var("reflect-odd", bcro)
mydata.create()
def test_vc_poisson_periodic(N,
store_bench=False,
comp_bench=False,
make_plot=False,
verbose=1):
"""
test the variable-coefficient MG solver. The return value
here is the error compared to the exact solution, UNLESS
comp_bench=True, in which case the return value is the
error compared to the stored benchmark
"""
# test the multigrid solver
nx = N
ny = nx
# create the coefficient variable
g = patch.Grid2d(nx, ny, ng=1)
d = patch.CellCenterData2d(g)
bc_c = bnd.BC(xlb="periodic",
xrb="periodic",
ylb="periodic",
yrb="periodic")
d.register_var("c", bc_c)
d.create()
c = d.get_var("c")
c[:, :] = alpha(g.x2d, g.y2d)
# check whether the RHS sums to zero (necessary for periodic data)
rhs = f(g.x2d, g.y2d)
print("rhs sum: {}".format(np.sum(rhs[g.ilo:g.ihi + 1, g.jlo:g.jhi + 1])))
# create the multigrid object
a = MG.VarCoeffCCMG2d(nx,
ny,
xl_BC_type="periodic",
yl_BC_type="periodic",
xr_BC_type="periodic",
yr_BC_type="periodic",
coeffs=c,
coeffs_bc=bc_c,
verbose=verbose,
vis=0,
true_function=true)
# initialize the solution to 0
a.init_zeros()
# initialize the RHS using the function f
rhs = f(a.x2d, a.y2d)
a.init_RHS(rhs)
# solve to a relative tolerance of 1.e-11
a.solve(rtol=1.e-11)
# alternately, we can just use smoothing by uncommenting the following
#a.smooth(a.nlevels-1,10000)
# get the solution
v = a.get_solution()
# get the true solution
b = true(a.x2d, a.y2d)
# compute the error from the analytic solution -- note that with
# periodic BCs all around, there is nothing to normalize the
# solution. We subtract off the average of phi from the MG
# solution (we do the same for the true solution to put them on
# the same footing)
e = v - np.sum(v.v()) / (nx * ny) - (
b - np.sum(b[a.ilo:a.ihi + 1, a.jlo:a.jhi + 1]) / (nx * ny))
enorm = e.norm()
print(" L2 error from true solution = %g\n rel. err from previous cycle = %g\n num. cycles = %d" % \
(enorm, a.relative_error, a.num_cycles))
# plot the solution
if make_plot:
plt.clf()
plt.figure(figsize=(10.0, 4.0), dpi=100, facecolor='w')
plt.subplot(121)
plt.imshow(np.transpose(v.v()),
interpolation="nearest",
origin="lower",
extent=[a.xmin, a.xmax, a.ymin, a.ymax])
plt.xlabel("x")
plt.ylabel("y")
plt.title("nx = {}".format(nx))
plt.colorbar()
plt.subplot(122)
plt.imshow(np.transpose(e.v()),
interpolation="nearest",
origin="lower",
extent=[a.xmin, a.xmax, a.ymin, a.ymax])
plt.xlabel("x")
plt.ylabel("y")
plt.title("error")
plt.colorbar()
plt.tight_layout()
plt.savefig("mg_vc_periodic_test.png")
# store the output for later comparison
bench = "mg_vc_poisson_periodic"
bench_dir = os.environ["PYRO_HOME"] + "/multigrid/tests/"
my_data = a.get_solution_object()
if store_bench:
my_data.write("{}/{}".format(bench_dir, bench))
# do we do a comparison?
if comp_bench:
compare_file = "{}/{}".format(bench_dir, bench)
msg.warning("comparing to {}".format(compare_file))
bench_grid, bench_data = patch.read(compare_file)
result = compare.compare(my_data.grid, my_data, bench_grid, bench_data)
if result == 0:
msg.success("results match benchmark\n")
else:
msg.warning("ERROR: {}\n".format(compare.errors[result]))
return result
# normal return -- error wrt true solution
return enorm
def initialize(self):
"""
Initialize the grid and variables for compressible flow and set
the initial conditions for the chosen problem.
"""
# setup the grid
nx = self.rp.get_param("mesh.nx")
ny = self.rp.get_param("mesh.ny")
xmin = self.rp.get_param("mesh.xmin")
xmax = self.rp.get_param("mesh.xmax")
ymin = self.rp.get_param("mesh.ymin")
ymax = self.rp.get_param("mesh.ymax")
verbose = self.rp.get_param("driver.verbose")
my_grid = patch.Grid2d(nx,
ny,
xmin=xmin,
xmax=xmax,
ymin=ymin,
ymax=ymax,
ng=4)
# create the variables
my_data = patch.CellCenterData2d(my_grid)
# define solver specific boundary condition routines
patch.define_bc("hse", BC.user)
# first figure out the boundary conditions. Note: the action
# can depend on the variable (for reflecting BCs)
xlb_type = self.rp.get_param("mesh.xlboundary")
xrb_type = self.rp.get_param("mesh.xrboundary")
ylb_type = self.rp.get_param("mesh.ylboundary")
yrb_type = self.rp.get_param("mesh.yrboundary")
bc = bnd.BC(xlb=xlb_type, xrb=xrb_type, ylb=ylb_type, yrb=yrb_type)
# density and energy
my_data.register_var("density", bc)
my_data.register_var("energy", bc)
my_data.register_var("erad", bc)
# for velocity, if we are reflecting, we need odd reflection
# in the normal direction.
# x-momentum -- if we are reflecting in x, then we need to
# reflect odd
bc_xodd = bnd.BC(xlb=xlb_type,
xrb=xrb_type,
ylb=ylb_type,
yrb=yrb_type,
odd_reflect_dir="x")
my_data.register_var("x-momentum", bc_xodd)
# y-momentum -- if we are reflecting in y, then we need to
# reflect odd
bc_yodd = bnd.BC(xlb=xlb_type,
xrb=xrb_type,
ylb=ylb_type,
yrb=yrb_type,
odd_reflect_dir="y")
my_data.register_var("y-momentum", bc_yodd)
# store grav because we'll need that in some BCs
my_data.set_aux("grav", self.rp.get_param("compressible.grav"))
my_data.create()
self.cc_data = my_data
self.ivars = Variables(idens=my_data.names.index("density"),
ixmom=my_data.names.index("x-momentum"),
iymom=my_data.names.index("y-momentum"),
iener=my_data.names.index("energy"),
ierad=my_data.names.index("erad"))
# initial conditions for the problem
problem = importlib.import_module("radhydro.problems.{}".format(
self.problem_name))
problem.init_data(self.cc_data, self.rp)
if verbose > 0: print(my_data)
def read(filename):
if not filename.endswith(".h5"):
filename += ".h5"
with h5py.File(filename, "r") as f:
# read the simulation information -- this only exists if the
# file was created as a simulation object
try:
solver_name = f.attrs["solver"]
problem_name = f.attrs["problem"]
t = f.attrs["time"]
n = f.attrs["nsteps"]
except KeyError:
# this was just a patch written out
solver_name = None
# read in the grid info and create our grid
grid = f["grid"].attrs
myg = patch.Grid2d(grid["nx"], grid["ny"], ng=grid["ng"],
xmin=grid["xmin"], xmax=grid["xmax"],
ymin=grid["ymin"], ymax=grid["ymax"])
# read in the variable info -- start by getting the names
gs = f["state"]
names = []
for n in gs:
names.append(n)
# create the CellCenterData2d object
myd = patch.CellCenterData2d(myg)
for n in names:
grp = gs[n]
bc = bnd.BC(xlb=grp.attrs["xlb"], xrb=grp.attrs["xrb"],
ylb=grp.attrs["ylb"], yrb=grp.attrs["yrb"])
myd.register_var(n, bc)
myd.create()
# auxillary data
for k in f["aux"].attrs:
myd.set_aux(k, f["aux"].attrs[k])
# restore the variable data
for n in names:
grp = gs[n]
data = grp["data"]
v = myd.get_var(n)
v.v()[:,:] = data[:,:]
if solver_name is not None:
solver = importlib.import_module(solver_name)
sim = solver.Simulation(solver_name, problem_name, None)
sim.n = n
sim.cc_data = myd
sim.cc_data.t = t
sim.read_extras(f)
if solver_name is not None:
return sim
else:
return myd
import numpy
import MG
import mesh.boundary as bnd
import mesh.patch as patch
nx = 128
ny = 128
nproj = 2
# create a mesh containing the x- and y-velocities, and periodic boundary
# conditions
myg = patch.Grid2d(nx, ny, ng=1)
bc = bnd.BC(xlb="periodic", xrb="periodic", ylb="periodic", yrb="periodic")
U = patch.CellCenterData2d(myg)
U.register_var('u-old', bc)
U.register_var('v-old', bc)
U.register_var('u+gphi', bc)
U.register_var('v+gphi', bc)
U.register_var('u', bc)
U.register_var('v', bc)
U.register_var('divU', bc)
U.register_var('phi-old', bc)
U.register_var('phi', bc)
U.register_var('dphi', bc)
def test_general_poisson_dirichlet(N,
store_bench=False,
comp_bench=False,
make_plot=False,
verbose=1):
"""
test the general MG solver. The return value
here is the error compared to the exact solution, UNLESS
comp_bench=True, in which case the return value is the
error compared to the stored benchmark
"""
# test the multigrid solver
nx = N
ny = nx
# create the coefficient variable
g = patch.Grid2d(nx, ny, ng=1)
d = patch.CellCenterData2d(g)
bc_c = bnd.BC(xlb="neumann", xrb="neumann", ylb="neumann", yrb="neumann")
d.register_var("alpha", bc_c)
d.register_var("beta", bc_c)
d.register_var("gamma_x", bc_c)
d.register_var("gamma_y", bc_c)
d.create()
a = d.get_var("alpha")
a[:, :] = alpha(g.x2d, g.y2d)
b = d.get_var("beta")
b[:, :] = beta(g.x2d, g.y2d)
gx = d.get_var("gamma_x")
gx[:, :] = gamma_x(g.x2d, g.y2d)
gy = d.get_var("gamma_y")
gy[:, :] = gamma_y(g.x2d, g.y2d)
# create the multigrid object
a = MG.GeneralMG2d(nx,
ny,
xl_BC_type="dirichlet",
yl_BC_type="dirichlet",
xr_BC_type="dirichlet",
yr_BC_type="dirichlet",
coeffs=d,
verbose=verbose,
vis=0,
true_function=true)
# initialize the solution to 0
a.init_zeros()
# initialize the RHS using the function f
rhs = f(a.x2d, a.y2d)
a.init_RHS(rhs)
# solve to a relative tolerance of 1.e-11
a.solve(rtol=1.e-11)
# alternately, we can just use smoothing by uncommenting the following
# a.smooth(a.nlevels-1,50000)
# get the solution
v = a.get_solution()
# compute the error from the analytic solution
b = true(a.x2d, a.y2d)
e = v - b
enorm = e.norm()
print(
" L2 error from true solution = %g\n rel. err from previous cycle = %g\n num. cycles = %d"
% (enorm, a.relative_error, a.num_cycles))
# plot the solution
if make_plot:
plt.clf()
plt.figure(figsize=(10.0, 4.0), dpi=100, facecolor='w')
plt.subplot(121)
plt.imshow(np.transpose(v.v()),
interpolation="nearest",
origin="lower",
extent=[a.xmin, a.xmax, a.ymin, a.ymax])
plt.xlabel("x")
plt.ylabel("y")
plt.title("nx = {}".format(nx))
plt.colorbar()
plt.subplot(122)
plt.imshow(np.transpose(e.v()),
interpolation="nearest",
origin="lower",
extent=[a.xmin, a.xmax, a.ymin, a.ymax])
plt.xlabel("x")
plt.ylabel("y")
plt.title("error")
plt.colorbar()
plt.tight_layout()
plt.savefig("mg_general_dirichlet_test.png")
# store the output for later comparison
bench = "mg_general_poisson_dirichlet"
bench_dir = os.environ["PYRO_HOME"] + "/multigrid/tests/"
my_data = a.get_solution_object()
if store_bench:
my_data.write("{}/{}".format(bench_dir, bench))
# do we do a comparison?
if comp_bench:
compare_file = "{}/{}".format(bench_dir, bench)
msg.warning("comparing to: %s " % (compare_file))
bench = io.read(compare_file)
result = compare.compare(my_data, bench)
if result == 0:
msg.success("results match benchmark\n")
else:
msg.warning("ERROR: " + compare.errors[result] + "\n")
return result
# normal return -- error wrt true solution
return enorm
# test the prolongation and restriction operations from the patch stuff
from __future__ import print_function
import mesh.boundary as bnd
import mesh.patch as patch
import numpy as np
# create our base grid and initialize it with sequential data
myg = patch.Grid2d(4,8,ng=1)
myd = patch.CellCenterData2d(myg)
bc = bnd.BC()
myd.register_var("a", bc)
myd.create()
a = myd.get_var("a")
a[myg.ilo:myg.ihi+1,myg.jlo:myg.jhi+1].flat = np.arange(myg.nx*myg.ny)
print("restriction test")
print("original (fine) array")
myd.pretty_print("a")
# create a coarse grid and fill the variable in it with restricted data
print(" ")
print("restricted array")
cg = patch.Grid2d(2,4,ng=1)
cd = patch.CellCenterData2d(cg)
cd.register_var("a", bc)
def __init__(self, nx, ny, ng=1,
xmin=0.0, xmax=1.0, ymin=0.0, ymax=1.0,
xl_BC_type="dirichlet", xr_BC_type="dirichlet",
yl_BC_type="dirichlet", yr_BC_type="dirichlet",
xl_BC=None, xr_BC=None,
yl_BC=None, yr_BC=None,
alpha=0.0, beta=-1.0,
nsmooth=10, nsmooth_bottom=50,
verbose=0,
aux_field=None, aux_bc=None,
true_function=None, vis=0, vis_title=""):
"""
Create the CellCenterMG2d object. Note that this requires a
grid to be a power of 2 in size and square.
Parameters
----------
nx : int
number of cells in x-direction
ny : int
number of cells in y-direction.
xmin : float, optional
minimum physical coordinate in x-direction
xmax : float, optional
maximum physical coordinate in x-direction
ymin : float, optional
minimum physical coordinate in y-direction
ymax : float, optional
maximum physical coordinate in y-direction
xl_BC_type : {'neumann', 'dirichlet', 'periodic'}, optional
boundary condition to enforce on lower x face
xr_BC_type : {'neumann', 'dirichlet', 'periodic'}, optional
boundary condition to enforce on upper x face
yl_BC_type : {'neumann', 'dirichlet', 'periodic'}, optional
boundary condition to enforce on lower y face
yr_BC_type : {'neumann', 'dirichlet', 'periodic'}, optional
boundary condition to enforce on upper y face
xl_BC : function, optional
function (of y) to call to get -x boundary values
(homogeneous assumed otherwise)
xr_BC : function, optional
function (of y) to call to get +x boundary values
(homogeneous assumed otherwise)
yl_BC : function, optional
function (of x) to call to get -y boundary values
(homogeneous assumed otherwise)
yr_BC : function, optional
function (of x) to call to get +y boundary values
(homogeneous assumed otherwise)
alpha : float, optional
coefficient in Helmholtz equation (alpha - beta L) phi = f
beta : float, optional
coefficient in Helmholtz equation (alpha - beta L) phi = f
nsmooth : int, optional
number of smoothing iterations to be done at each intermediate
level in the V-cycle (up and down)
nsmooth_bottom : int, optional
number of smoothing iterations to be done during the bottom
solve
verbose : int, optional
increase verbosity during the solve (for verbose=1)
aux_field : list of str, optional
extra fields to define and carry at each level.
Useful for subclassing.
aux_bc : list of BC objects, optional
the boundary conditions corresponding to the aux fields
true_function : function, optional
a function (of x,y) that provides the exact solution to
the elliptic problem we are solving. This is used only
for visualization purposes
vis : int, optional
output a detailed visualization of every smoothing step
all throughout the V-cycle (if vis=1)
vis_title : string, optional
a descriptive title to write on the visualization plots
Returns
-------
out: CellCenterMG2d object
"""
if nx != ny:
raise ValueError("ERROR: multigrid currently requires nx = ny")
self.nx = nx
self.ny = ny
self.ng = ng
self.xmin = xmin
self.xmax = xmax
self.ymin = ymin
self.ymax = ymax
if (xmax-xmin) != (ymax-ymin):
raise ValueError("ERROR: multigrid currently requires a square domain")
self.alpha = alpha
self.beta = beta
self.nsmooth = nsmooth
self.nsmooth_bottom = nsmooth_bottom
self.max_cycles = 100
self.verbose = verbose
# for visualization purposes, we can set a function name that
# provides the true solution to our elliptic problem.
if true_function is not None:
self.true_function = true_function
# a small number used in computing the error, so we don't divide by 0
self.small = 1.e-16
# keep track of whether we've initialized the RHS
self.initialized_rhs = 0
# assume that self.nx = 2^(nlevels-1) and that nx = ny
# this defines nlevels such that we end exactly on a 2x2 grid
self.nlevels = int(math.log(self.nx)/math.log(2.0))
# a multigrid object will be a list of grids
self.grids = []
# create the grids. Here, self.grids[0] will be the coarsest
# grid and self.grids[nlevel-1] will be the finest grid
# we store the solution, v, the rhs, f.
# create the boundary condition object
bc = bnd.BC(xlb=xl_BC_type, xrb=xr_BC_type,
ylb=yl_BC_type, yrb=yr_BC_type)
nx_t = ny_t = 2
for i in range(self.nlevels):
# create the grid
my_grid = patch.Grid2d(nx_t, ny_t, ng=self.ng,
xmin=xmin, xmax=xmax, ymin=ymin, ymax=ymax)
# add a CellCenterData2d object for this level to our list
self.grids.append(patch.CellCenterData2d(my_grid, dtype=np.float64))
# create the phi BC object -- this only applies for the finest
# level. On the coarser levels, phi represents the residual,
# which has homogeneous BCs
bc_p = bnd.BC(xlb=xl_BC_type, xrb=xr_BC_type,
ylb=yl_BC_type, yrb=yr_BC_type,
xl_func=xl_BC, xr_func=xr_BC,
yl_func=yl_BC, yr_func=yr_BC, grid=my_grid)
if i == self.nlevels-1:
self.grids[i].register_var("v", bc_p)
else:
self.grids[i].register_var("v", bc)
self.grids[i].register_var("f", bc)
self.grids[i].register_var("r", bc)
if aux_field is not None:
for f, b in zip(aux_field, aux_bc):
self.grids[i].register_var(f, b)
self.grids[i].create()
if self.verbose:
print(self.grids[i])
nx_t = nx_t*2
ny_t = ny_t*2
# provide coordinate and indexing information for the solution mesh
soln_grid = self.grids[self.nlevels-1].grid
self.ilo = soln_grid.ilo
self.ihi = soln_grid.ihi
self.jlo = soln_grid.jlo
self.jhi = soln_grid.jhi
self.x = soln_grid.x
self.dx = soln_grid.dx
self.x2d = soln_grid.x2d
self.y = soln_grid.y
self.dy = soln_grid.dy # note, dy = dx is assumed
self.y2d = soln_grid.y2d
self.soln_grid = soln_grid
# store the source norm
self.source_norm = 0.0
# after solving, keep track of the number of cycles taken, the
# relative error from the previous cycle, and the residual error
# (normalized to the source norm)
self.num_cycles = 0
self.residual_error = 1.e33
self.relative_error = 1.e33
# keep track of where we are in the V
self.current_cycle = -1
self.current_level = -1
self.up_or_down = ""
# for visualization -- what frame are we outputting?
self.vis = vis
self.vis_title = vis_title
self.frame = 0
def doit(nx, ny):
nproj = 2
# create a mesh containing the x- and y-velocities, and periodic boundary
# conditions
myg = patch.Grid2d(nx, ny, ng=1)
bc = bnd.BC(xlb="periodic", xrb="periodic", ylb="periodic", yrb="periodic")
U = patch.CellCenterData2d(myg)
U.register_var('u-old', bc)
U.register_var('v-old', bc)
U.register_var('u+gphi', bc)
U.register_var('v+gphi', bc)
U.register_var('u', bc)
U.register_var('v', bc)
U.register_var('divU', bc)
U.register_var('phi-old', bc)
U.register_var('phi', bc)
U.register_var('dphi', bc)
U.register_var('gradphi_x-old', bc)
U.register_var('gradphi_y-old', bc)
U.register_var('gradphi_x', bc)
U.register_var('gradphi_y', bc)
U.create()
# initialize a divergence free velocity field,
# u = -sin^2(pi x) sin(2 pi y), v = sin^2(pi y) sin(2 pi x)
u = U.get_var('u')
v = U.get_var('v')
u[:, :] = -(np.sin(np.pi * myg.x2d)**2) * np.sin(2.0 * np.pi * myg.y2d)
v[:, :] = (np.sin(np.pi * myg.y2d)**2) * np.sin(2.0 * np.pi * myg.x2d)
# store the original, divergence free velocity field for comparison later
uold = U.get_var('u-old')
vold = U.get_var('v-old')
uold[:, :] = u.copy()
vold[:, :] = v.copy()
# the projection routine should decompose U into a divergence free
# part, U_d, plus the gradient of a scalar. Add on the gradient
# of a scalar that satisfies gradphi.n = 0. After the projection,
# we should recover the divergence free field above. Take phi to
# be a gaussian, exp(-((x-x0)^2 + (y-y0)^2)/R)
R = 0.1
x0 = 0.5
y0 = 0.5
phi = U.get_var('phi-old')
gradphi_x = U.get_var('gradphi_x-old')
gradphi_y = U.get_var('gradphi_y-old')
phi[:, :] = np.exp(-((myg.x2d - x0)**2 + (myg.y2d - y0)**2) / R**2)
gradphi_x[:, :] = phi * (-2.0 * (myg.x2d - x0) / R**2)
gradphi_y[:, :] = phi * (-2.0 * (myg.y2d - y0) / R**2)
u += gradphi_x
v += gradphi_y
u_plus_gradphi = U.get_var('u+gphi')
v_plus_gradphi = U.get_var('v+gphi')
u_plus_gradphi[:, :] = u[:, :]
v_plus_gradphi[:, :] = v[:, :]
# use the mesh class to enforce the periodic BCs on the velocity field
U.fill_BC_all()
# now compute the cell-centered, centered-difference divergence
divU = U.get_var('divU')
divU[myg.ilo:myg.ihi+1, myg.jlo:myg.jhi+1] = \
0.5*(u[myg.ilo+1:myg.ihi+2, myg.jlo:myg.jhi+1] -
u[myg.ilo-1:myg.ihi, myg.jlo:myg.jhi+1])/myg.dx + \
0.5*(v[myg.ilo:myg.ihi+1, myg.jlo+1:myg.jhi+2] -
v[myg.ilo:myg.ihi+1, myg.jlo-1:myg.jhi])/myg.dy
# create the multigrid object with Neumann BCs
a = MG.CellCenterMG2d(nx,
ny,
xl_BC_type="periodic",
xr_BC_type="periodic",
yl_BC_type="periodic",
yr_BC_type="periodic",
verbose=1)
#--------------------------------------------------------------------------
# projections
#--------------------------------------------------------------------------
for iproj in range(nproj):
a.init_zeros()
a.init_RHS(divU)
a.solve(rtol=1.e-12)
phi = U.get_var('phi')
solution = a.get_solution()
phi[myg.ilo-1:myg.ihi+2, myg.jlo-1:myg.jhi+2] = \
solution[a.ilo-1:a.ihi+2, a.jlo-1:a.jhi+2]
dphi = U.get_var('dphi')
dphi[:, :] = phi - U.get_var('phi-old')
# compute the gradient of phi using centered differences
gradphi_x = U.get_var('gradphi_x')
gradphi_y = U.get_var('gradphi_y')
gradphi_x[myg.ilo:myg.ihi+1, myg.jlo:myg.jhi+1] = \
0.5*(phi[myg.ilo+1:myg.ihi+2, myg.jlo:myg.jhi+1] -
phi[myg.ilo-1:myg.ihi, myg.jlo:myg.jhi+1])/myg.dx
gradphi_y[myg.ilo:myg.ihi+1, myg.jlo:myg.jhi+1] = \
0.5*(phi[myg.ilo:myg.ihi+1, myg.jlo+1:myg.jhi+2] -
phi[myg.ilo:myg.ihi+1, myg.jlo-1:myg.jhi])/myg.dy
# update the velocity field
u -= gradphi_x
v -= gradphi_y
U.fill_BC_all()
# recompute the divergence diagnostic
divU[myg.ilo:myg.ihi+1, myg.jlo:myg.jhi+1] = \
0.5*(u[myg.ilo+1:myg.ihi+2, myg.jlo:myg.jhi+1] -
u[myg.ilo-1:myg.ihi, myg.jlo:myg.jhi+1])/myg.dx + \
0.5*(v[myg.ilo:myg.ihi+1, myg.jlo+1:myg.jhi+2] -
v[myg.ilo:myg.ihi+1, myg.jlo-1:myg.jhi])/myg.dy
U.write("proj-periodic.after" + ("%d" % iproj))