def _verify_moments(self, grid, order):
bgk = sym_equilibrium.bgk_equilibrium(grid, cfg, order=order)
rho_ex = 0
momentum = [0, 0, 0]
for ex, ei in zip(bgk.expression, grid.basis):
rho_ex += ex
for i, ei_c in enumerate(ei):
momentum[i] += ei_c * ex
self.assertEqual(sympy.simplify(rho_ex), sym.S.rho)
self.assertEqual(sympy.simplify(momentum[0]), sym.S.rho * sym.S.vx)
self.assertEqual(sympy.simplify(momentum[1]), sym.S.rho * sym.S.vy)
if grid.dim == 3:
self.assertEqual(sympy.simplify(momentum[2]), sym.S.rho * sym.S.vz)
def _verify_moments(self, grid, order):
bgk = sym_equilibrium.bgk_equilibrium(grid, cfg, order=order)
rho_ex = 0
momentum = [0, 0, 0]
for ex, ei in zip(bgk.expression, grid.basis):
rho_ex += ex
for i, ei_c in enumerate(ei):
momentum[i] += ei_c * ex
self.assertEqual(sympy.simplify(rho_ex), sym.S.rho)
self.assertEqual(sympy.simplify(momentum[0]), sym.S.rho * sym.S.vx)
self.assertEqual(sympy.simplify(momentum[1]), sym.S.rho * sym.S.vy)
if grid.dim == 3:
self.assertEqual(sympy.simplify(momentum[2]), sym.S.rho * sym.S.vz)
def test_d3q19_2nd_order_bgk(self):
"""Verifies that the entropic equilibrium for D3Q19 is the same
as the LBGK equilibrium up to 2nd order in velocity."""
grid = sym.D3Q19
bgk = sym_equilibrium.bgk_equilibrium(grid, cfg)
elbm = sym_equilibrium.elbm_d3q19_equilibrium(grid, order=2)
for i, (elbm_ex, bgk_ex) in enumerate(zip(elbm.expression, bgk.expression)):
for x in elbm.local_vars:
elbm_ex = elbm_ex.subs({x.lhs: x.rhs})
elbm_trunc = sym_codegen.truncate_velocity(Poly(elbm_ex), order=2).subs({
'vsq': sym.S.vx**2 + sym.S.vy**2 + sym.S.vz**2})
self.assertEqual(elbm_trunc.expand(), bgk_ex.expand(),
'%d component' % i)
def test_d3q19_2nd_order_bgk(self):
"""Verifies that the entropic equilibrium for D3Q19 is the same
as the LBGK equilibrium up to 2nd order in velocity."""
grid = sym.D3Q19
bgk = sym_equilibrium.bgk_equilibrium(grid, cfg)
elbm = sym_equilibrium.elbm_d3q19_equilibrium(grid, order=2)
for i, (elbm_ex,
bgk_ex) in enumerate(zip(elbm.expression, bgk.expression)):
for x in elbm.local_vars:
elbm_ex = elbm_ex.subs({x.lhs: x.rhs})
elbm_trunc = sym_codegen.truncate_velocity(
Poly(elbm_ex),
order=2).subs({'vsq': sym.S.vx**2 + sym.S.vy**2 + sym.S.vz**2})
self.assertEqual(elbm_trunc.expand(), bgk_ex.expand(),
'%d component' % i)
def test_TMS(self):
settings = {
'debug_single_process': True,
'quiet': True,
'precision': 'double',
'access_pattern': 'AB',
'check_invalid_results_gpu': False,
'check_invalid_results_host': False,
'lat_nx': self.nx,
'lat_ny': self.ny,
'max_iters': 1,
'visc': 1.0 / 12.0,
}
ctrl = LBSimulationController(Test2DSim, default_config=settings)
ctrl.run(ignore_cmdline=True)
runner = ctrl.master.runner
dist = runner._debug_get_dist()
rho_bb = 0.0
ux_bb = 0.0
uy_bb = 0.0
for k, v in fi_start_2d.iteritems():
if D2Q9.basis[k][1] == 1:
v = fi_start_2d[D2Q9.idx_opposite[k]]
rho_bb += v
ux_bb += D2Q9.basis[k][0] * v
uy_bb += D2Q9.basis[k][1] * v
ux_bb /= rho_bb
uy_bb /= rho_bb
rho = 0.0
ux = 0.0
uy = 0.0
cfg = LBConfig()
cfg.incompressible = False
cfg.minimize_roundoff = False
eq = bgk_equilibrium(D2Q9, cfg).expression
for k, v in fi_start_2d.iteritems():
if D2Q9.basis[k][1] == 1:
v = eq[k].evalf(subs={
'g0m0': rho_bb,
'g0m1x': ux_bb,
'g0m1y': uy_bb
})
rho += v
ux += D2Q9.basis[k][0] * v
uy += D2Q9.basis[k][1] * v
ux /= rho
uy /= rho
print 'Target values are rho=%e, ux=%e, uy=%e' % (rho_bb, ux_bb, uy_bb)
print 'Instantaneous values are rho=%e, ux=%e, uy=%e' % (rho, ux, uy)
fneq = {}
for k, v in fi_start_2d.iteritems():
if D2Q9.basis[k][1] == 1:
fneq[k] = (eq[k].evalf(subs={
'g0m0': rho_bb,
'g0m1x': ux_bb,
'g0m1y': uy_bb
}) - eq[k].evalf(subs={
'g0m0': rho,
'g0m1x': ux,
'g0m1y': uy
}))
else:
fneq[k] = v - eq[k].evalf(subs={
'g0m0': rho,
'g0m1x': ux,
'g0m1y': uy
})
tau = relaxation_time(1.0 / 12.0)
omega = 1.0 / tau
res = {}
for k, v in fi_start_2d.iteritems():
if D2Q9.basis[k][1] == 1:
res[k] = ((1.0 - (omega - 1)) * eq[k].evalf(subs={
'g0m0': rho_bb,
'g0m1x': ux_bb,
'g0m1y': uy_bb
}) + (omega - 1) * eq[k].evalf(subs={
'g0m0': rho,
'g0m1x': ux,
'g0m1y': uy
}))
else:
res[k] = (v + omega * (eq[k].evalf(subs={
'g0m0': rho,
'g0m1x': ux,
'g0m1y': uy
}) - v) + eq[k].evalf(subs={
'g0m0': rho_bb,
'g0m1x': ux_bb,
'g0m1y': uy_bb
}) - eq[k].evalf(subs={
'g0m0': rho,
'g0m1x': ux,
'g0m1y': uy
}))
for k, v in res.iteritems():
np.testing.assert_allclose(dist[k, 1, 16], np.float64(v))
def test_TMS(self):
settings = {
'debug_single_process': True,
'quiet': True,
'precision': 'double',
'access_pattern': 'AB',
'check_invalid_results_gpu': False,
'check_invalid_results_host': False,
'lat_nx': self.nx,
'lat_ny': self.ny,
'max_iters': 1,
'visc': 1.0/12.0,
}
ctrl = LBSimulationController(Test2DSim, default_config=settings)
ctrl.run(ignore_cmdline=True)
runner = ctrl.master.runner
dist = runner._debug_get_dist()
rho_bb = 0.0
ux_bb = 0.0
uy_bb = 0.0
for k, v in fi_start_2d.iteritems():
if D2Q9.basis[k][1] == 1:
v = fi_start_2d[D2Q9.idx_opposite[k]]
rho_bb += v
ux_bb += D2Q9.basis[k][0] * v
uy_bb += D2Q9.basis[k][1] * v
ux_bb /= rho_bb
uy_bb /= rho_bb
rho = 0.0
ux = 0.0
uy = 0.0
cfg = LBConfig()
cfg.incompressible = False
cfg.minimize_roundoff = False
eq = bgk_equilibrium(D2Q9, cfg).expression
for k, v in fi_start_2d.iteritems():
if D2Q9.basis[k][1] == 1:
v = eq[k].evalf(subs={'g0m0': rho_bb, 'g0m1x': ux_bb,
'g0m1y': uy_bb})
rho += v
ux += D2Q9.basis[k][0] * v
uy += D2Q9.basis[k][1] * v
ux /= rho
uy /= rho
print 'Target values are rho=%e, ux=%e, uy=%e' % (rho_bb, ux_bb, uy_bb)
print 'Instantaneous values are rho=%e, ux=%e, uy=%e' % (rho, ux, uy)
fneq = {}
for k, v in fi_start_2d.iteritems():
if D2Q9.basis[k][1] == 1:
fneq[k] = (eq[k].evalf(subs={'g0m0': rho_bb, 'g0m1x': ux_bb, 'g0m1y': uy_bb}) -
eq[k].evalf(subs={'g0m0': rho, 'g0m1x': ux, 'g0m1y': uy}))
else:
fneq[k] = v - eq[k].evalf(subs={'g0m0': rho, 'g0m1x': ux, 'g0m1y': uy})
tau = relaxation_time(1.0/12.0)
omega = 1.0 / tau
res = {}
for k, v in fi_start_2d.iteritems():
if D2Q9.basis[k][1] == 1:
res[k] = ((1.0 - (omega - 1)) *
eq[k].evalf(subs={'g0m0': rho_bb, 'g0m1x': ux_bb, 'g0m1y': uy_bb}) +
(omega - 1) * eq[k].evalf(subs={'g0m0': rho, 'g0m1x': ux, 'g0m1y': uy}))
else:
res[k] = (v + omega * (eq[k].evalf(subs={'g0m0': rho, 'g0m1x': ux, 'g0m1y': uy}) - v) +
eq[k].evalf(subs={'g0m0': rho_bb, 'g0m1x': ux_bb, 'g0m1y': uy_bb}) -
eq[k].evalf(subs={'g0m0': rho, 'g0m1x': ux, 'g0m1y': uy}))
for k, v in res.iteritems():
np.testing.assert_allclose(dist[k,1,16], np.float64(v))
