test_fluctuating_lb.py 8.79 KB
Newer Older
1
"""Tests velocity and stress fluctuations for thermalized LB"""
2
3
4


import pystencils as ps
5
6
from lbmpy.creationfunctions import *
from lbmpy.macroscopic_value_kernels import macroscopic_values_setter
7
import numpy as np
8
from lbmpy.moments import is_bulk_moment, is_shear_moment, get_order
9
10


11
def single_component_maxwell(x1, x2, kT, mass):
12
13
    """Integrate the probability density from x1 to x2 using the trapezoidal rule"""
    x = np.linspace(x1, x2, 1000)
14
15
16
17
    return np.trapz(np.exp(-mass * x**2 / (2. * kT)), x) / np.sqrt(2. * np.pi * kT/mass)


def rr_getter(moment_group):
18
19
20
    """Maps a group of moments to a relaxation rate (shear, bulk, even, odd)
    in the 4 relaxation time thermalized LB model
    """
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
    is_shear = [is_shear_moment(m, 3) for m in moment_group]
    is_bulk = [is_bulk_moment(m, 3) for m in moment_group]
    order = [get_order(m) for m in moment_group]
    assert min(order) == max(order)
    order = order[0]

    if order < 2:
        return 0
    elif any(is_bulk):
        assert all(is_bulk)
        return sp.Symbol("omega_bulk")
    elif any(is_shear):
        assert all(is_shear)
        return sp.Symbol("omega_shear")
    elif order % 2 == 0:
        assert order > 2
        return sp.Symbol("omega_even")
    else:
        return sp.Symbol("omega_odd")


def second_order_moment_tensor_assignments(function_values, stencil, output_field):
    """Assignments for calculating the pressure tensor"""
    assert len(function_values) == len(stencil)
    dim = len(stencil[0])
    return [ps.Assignment(output_field(i, j),
                          sum(c[i] * c[j] * f for f, c in zip(function_values, stencil)))
            for i in range(dim) for j in range(dim)]


def add_pressure_output_to_collision_rule(collision_rule, pressure_field):
    pressure_ouput = second_order_moment_tensor_assignments(collision_rule.method.pre_collision_pdf_symbols,
                                                            collision_rule.method.stencil, pressure_field)
    collision_rule.main_assignments = collision_rule.main_assignments + pressure_ouput


57
def get_fluctuating_lb(size=None, kT=None, omega_shear=None, omega_bulk=None, omega_odd=None, omega_even=None, rho_0=None, target=None):
58
59
60
61
62

    # Parameters
    stencil = get_stencil('D3Q19')

    # Setup data handling
63
64
    dh = ps.create_data_handling(
        [size]*3, periodicity=True, default_target=target)
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
    src = dh.add_array('src', values_per_cell=len(stencil), layout='f')
    dst = dh.add_array_like('dst', 'src')
    rho = dh.add_array('rho', layout='f', latex_name='\\rho')
    u = dh.add_array('u', values_per_cell=dh.dim, layout='f')
    pressure_field = dh.add_array('pressure', values_per_cell=(
        3, 3), layout='f', gpu=target == 'gpu')
    force_field = dh.add_array(
        'force', values_per_cell=3, layout='f', gpu=target == 'gpu')

    # Method setup
    method = create_mrt_orthogonal(
        stencil=get_stencil('D3Q19'),
        compressible=True,
        weighted=True,
        relaxation_rate_getter=rr_getter,
80
        force_model=force_model_from_string('schiller', force_field.center_vector))
81
82
83
84
85
86
    collision_rule = create_lb_collision_rule(
        method,
        fluctuating={
            'temperature': kT
        },
        optimization={'cse_global': True}
87
88
    )

89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
    add_pressure_output_to_collision_rule(collision_rule, pressure_field)

    collision = create_lb_update_rule(collision_rule=collision_rule,
                                      stencil=stencil,
                                      method=method,
                                      compressible=True,
                                      kernel_type='collide_only',
                                      optimization={'symbolic_field': src})
    stream = create_stream_pull_with_output_kernel(collision.method, src, dst,
                                                   {'density': rho, 'velocity': u})

    opts = {'cpu_openmp': True,
            'cpu_vectorize_info': None,
            'target': dh.default_target}

    # Compile kernels
    stream_kernel = ps.create_kernel(stream, **opts).compile()
    collision_kernel = ps.create_kernel(collision, **opts).compile()

    sync_pdfs = dh.synchronization_function([src.name])

    # Initialization
    init = macroscopic_values_setter(collision.method, velocity=(0,)*dh.dim,
                                     pdfs=src.center_vector, density=rho.center)
    init_kernel = ps.create_kernel(init, ghost_layers=0).compile()

    dh.fill(rho.name, rho_0)
    dh.fill(u.name, np.nan, ghost_layers=True, inner_ghost_layers=True)
    dh.fill(u.name, 0)
118
119
120
    dh.fill(force_field.name, np.nan,
            ghost_layers=True, inner_ghost_layers=True)
    dh.fill(force_field.name, 0)
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
    dh.run_kernel(init_kernel)

    # time loop
    def time_loop(start, steps):
        dh.all_to_gpu()
        for i in range(start, start+steps):
            dh.run_kernel(collision_kernel, omega_shear=omega_shear, omega_bulk=omega_bulk,
                          omega_odd=omega_odd, omega_even=omega_even, seed=42, time_step=i)

            sync_pdfs()
            dh.run_kernel(stream_kernel)

            dh.swap(src.name, dst.name)
        return start+steps

136
137
138
    return dh, time_loop


139
def test_resting_fluid(target="cpu"):
140
141
142
    rho_0 = 0.86
    kT = 4E-4
    L = [60]*3
143
    dh, time_loop = get_fluctuating_lb(size=L[0], target=target,
144
145
146
                                       rho_0=rho_0, kT=kT,
                                       omega_shear=0.8, omega_bulk=0.5, omega_even=.04, omega_odd=0.3)

147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
    # Test
    t = 0
    # warm up
    t = time_loop(t, 10)

    # Measurement
    for i in range(10):
        t = time_loop(t, 5)

        res_u = dh.gather_array("u").reshape((-1, 3))
        res_rho = dh.gather_array("rho").reshape((-1,))

        # mass conservation
        np.testing.assert_allclose(np.mean(res_rho), rho_0, atol=3E-12)

        # momentum conservation
        momentum = np.dot(res_rho, res_u)
        np.testing.assert_allclose(momentum, [0, 0, 0], atol=1E-10)

        # temperature
        kinetic_energy = 1/2*np.dot(res_rho, res_u*res_u)/np.product(L)
        np.testing.assert_allclose(
            kinetic_energy, [kT/2]*3, atol=kT*0.01)

        # velocity distribution
        v_hist, v_bins = np.histogram(
            res_u, bins=11, range=(-.075, .075), density=True)

        # Calculate expected values from single
        v_expected = []
        for j in range(len(v_hist)):
            # Maxwell distribution
            res = 1./(v_bins[j+1]-v_bins[j]) * \
                single_component_maxwell(
                    v_bins[j], v_bins[j+1], kT, rho_0)
            v_expected.append(res)
        v_expected = np.array(v_expected)

        # 10% accuracy on the entire histogram
        np.testing.assert_allclose(v_hist, v_expected, rtol=0.1)
        # 1% accuracy on the middle part
        remove = 3
        np.testing.assert_allclose(
            v_hist[remove:-remove], v_expected[remove:-remove], rtol=0.01)

        # pressure tensor against expressions from
        # Duenweg, Schiller, Ladd, https://arxiv.org/abs/0707.1581

        res_pressure = dh.gather_array("pressure").reshape((-1, 3, 3))

        c_s = np.sqrt(1/3)  # speed of sound

        # average of pressure tensor
        # Diagonal elements are rho c_s^22 +<u,u>. When the fluid is
        # thermalized, the expectation value of <u,u> = kT due to the
        # equi-partition theorem.
        p_av_expected = np.diag([rho_0*c_s**2 + kT]*3)
        np.testing.assert_allclose(
            np.mean(res_pressure, axis=0), p_av_expected, atol=c_s**2/2000)
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244


def test_point_force(target="cpu"):
    """Test momentum balance for thermalized fluid with applied poitn forces"""
    rho_0 = 0.86
    kT = 4E-4
    L = [8]*3
    dh, time_loop = get_fluctuating_lb(size=L[0], target=target,
                                       rho_0=rho_0, kT=kT,
                                       omega_shear=0.8, omega_bulk=0.5, omega_even=.04, omega_odd=0.3)

    # Test
    t = 0
    # warm up
    t = time_loop(t, 100)

    introduced_momentum = np.zeros(3)
    for i in range(100):
        point_force = 1E-5*(np.random.random(3) - .5)
        introduced_momentum += point_force

        # Note that ghost layers are included in the indexing
        force_pos = np.random.randint(1, L[0]-2, size=3)

        dh.cpu_arrays["force"][force_pos[0],
                               force_pos[1], force_pos[2]] = point_force
        t = time_loop(t, 1)
        res_u = dh.gather_array("u").reshape((-1, 3))
        res_rho = dh.gather_array("rho").reshape((-1,))

        # mass conservation
        np.testing.assert_allclose(np.mean(res_rho), rho_0, atol=3E-12)

        # momentum conservation
        momentum = np.dot(res_rho, res_u)
        np.testing.assert_allclose(
            momentum, introduced_momentum + 0.5 * point_force, atol=1E-10)
        dh.cpu_arrays["force"][force_pos[0],
                               force_pos[1], force_pos[2]] = np.zeros(3)