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example_streamlines.py
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369 lines (302 loc) · 12.1 KB
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# SPDX-FileCopyrightText: Copyright (c) 2024 NVIDIA CORPORATION & AFFILIATES. All rights reserved.
# SPDX-License-Identifier: Apache-2.0
###########################################################################
# Example Streamlines
#
# Shows how to generate 3D streamlines by tracing through a velocity field
# using the `warp.fem.lookup` operator.
# Also illustrates using `warp.fem.Subdomain` to define subsets of elements.
#
###########################################################################
import numpy as np
import warp as wp
import warp.examples.fem.utils as fem_example_utils
import warp.fem as fem
from warp._src.utils import warn
from warp.examples.fem.example_apic_fluid import divergence_form, solve_incompressibility
def bourke_color_map(low, high, v):
c = [1.0, 1.0, 1.0]
if v < low:
v = low
if v > high:
v = high
dv = high - low
if v < (low + 0.25 * dv):
c[0] = 0.0
c[1] = 4.0 * (v - low) / dv
elif v < (low + 0.5 * dv):
c[0] = 0.0
c[2] = 1.0 + 4.0 * (low + 0.25 * dv - v) / dv
elif v < (low + 0.75 * dv):
c[0] = 4.0 * (v - low - 0.5 * dv) / dv
c[2] = 0.0
else:
c[1] = 1.0 + 4.0 * (low + 0.75 * dv - v) / dv
c[2] = 0.0
return c
@fem.integrand
def classify_boundary_sides(
s: fem.Sample,
domain: fem.Domain,
outflow: wp.array[int],
freeslip: wp.array[int],
inflow: wp.array[int],
):
x = fem.position(domain, s)
n = fem.normal(domain, s)
if n[0] < -0.5:
# left side
inflow[s.qp_index] = 1
elif n[0] > 0.5:
if x[1] > 0.33 or x[2] < 0.33:
# right side, top
freeslip[s.qp_index] = 1
else:
# right side, bottom
outflow[s.qp_index] = 1
else:
freeslip[s.qp_index] = 1
@fem.integrand
def inflow_velocity(
s: fem.Sample,
domain: fem.Domain,
):
n = fem.normal(domain, s)
return -n
@fem.integrand
def noslip_projector_form(
s: fem.Sample,
u: fem.Field,
v: fem.Field,
):
return wp.dot(u(s), v(s))
@fem.integrand
def freeslip_projector_form(
s: fem.Sample,
domain: fem.Domain,
u: fem.Field,
v: fem.Field,
):
n = fem.normal(domain, s)
return wp.dot(u(s), n) * wp.dot(n, v(s))
@fem.integrand
def mass_form(
s: fem.Sample,
u: fem.Field,
v: fem.Field,
):
return wp.dot(u(s), v(s))
@fem.integrand
def spawn_streamlines(s: fem.Sample, domain: fem.Domain, jitter: float):
rng = wp.rand_init(s.qp_index)
random_offset = wp.vec3(wp.randf(rng), wp.randf(rng), wp.randf(rng)) - wp.vec3(0.5)
# remove jistter along normal
n = fem.normal(domain, s)
random_offset -= wp.dot(random_offset, n) * n
return domain(s) + jitter * random_offset
@fem.integrand
def gen_streamlines(
s: fem.Sample,
domain: fem.Domain,
u: fem.Field,
spawn_points: wp.array[wp.vec3],
point_count: int,
dx: float,
pos: wp.array2d[wp.vec3],
speed: wp.array2d[float],
):
idx = s.qp_index
p = spawn_points[idx]
s = fem.lookup(domain, p)
for k in range(point_count):
v = u(s)
pos[idx, k] = p
speed[idx, k] = wp.length(v)
flow_dir = wp.normalize(v)
adv_p = p + flow_dir * dx
adv_s = fem.lookup(domain, adv_p, s)
if adv_s.element_index != fem.NULL_ELEMENT_INDEX:
# if the lookup result position is different from adv_p,
# it means we have been projected back onto the domain;
# align back with flow and terminate streamline
new_p = domain(adv_s)
if wp.length_sq(new_p - adv_p) > 0.000001:
p = p + wp.dot(new_p - p, flow_dir) * flow_dir
s = fem.lookup(domain, p, s)
dx = 0.0
else:
s = adv_s
p = new_p
class Example:
def __init__(self, quiet=False, degree=2, resolution=16, mesh="grid", headless: bool = False):
self._quiet = quiet
self._degree = degree
self._streamline_dx = 0.5 / resolution
self._streamline_point_count = 4 * resolution
res = wp.vec3i(resolution)
if mesh == "tet":
pos, tet_vtx_indices = fem_example_utils.gen_tetmesh(
res=res,
)
self._geo = fem.Tetmesh(tet_vtx_indices, pos, build_bvh=True)
elif mesh == "hex":
pos, hex_vtx_indices = fem_example_utils.gen_hexmesh(
res=res,
)
self._geo = fem.Hexmesh(hex_vtx_indices, pos, assume_parallelepiped_cells=True, build_bvh=True)
elif mesh == "nano":
volume = fem_example_utils.gen_volume(
res=res,
)
self._geo = fem.Nanogrid(volume)
else:
self._geo = fem.Grid3D(
res=res,
)
# Mark sides with boundary conditions that should apply
boundary = fem.BoundarySides(self._geo)
inflow_mask = wp.zeros(shape=boundary.element_count(), dtype=int)
freeslip_mask = wp.zeros(shape=boundary.element_count(), dtype=int)
outflow_mask = wp.zeros(shape=boundary.element_count(), dtype=int)
fem.interpolate(
classify_boundary_sides,
at=boundary,
values={"outflow": outflow_mask, "freeslip": freeslip_mask, "inflow": inflow_mask},
)
self._inflow = fem.Subdomain(boundary, element_mask=inflow_mask)
self._freeslip = fem.Subdomain(boundary, element_mask=freeslip_mask)
self._outflow = fem.Subdomain(boundary, element_mask=outflow_mask)
self.plot = fem_example_utils.Plot()
self.renderer = None
if not headless:
try:
self.renderer = wp.render.OpenGLRenderer(
camera_pos=(2.0, 0.5, 3.0),
camera_front=(-0.66, 0.0, -1.0),
draw_axis=False,
)
except Exception as err:
warn(f"Could not initialize OpenGL renderer: {err}")
pass
def step(self):
self._generate_incompressible_flow()
# first generate spawn points for the streamlines
# we do this by regularly sampling the inflow boundary with a small amount of jitter
streamline_spawn = fem.RegularQuadrature(
domain=self._inflow, order=self._degree, family=fem.Polynomial.GAUSS_LEGENDRE
)
n_streamlines = streamline_spawn.total_point_count()
spawn_points = wp.empty(dtype=wp.vec3, shape=n_streamlines)
jitter_amount = self._streamline_dx / self._degree
fem.interpolate(spawn_streamlines, dest=spawn_points, at=streamline_spawn, values={"jitter": jitter_amount})
# now forward-trace the velocity field to generate the streamlines
# here we use a fixed number of points per streamline, otherwise we would need to
# do a first pass to count points, then array_scan the offsets, then a second pass
# to populate the per-point data
point_count = self._streamline_point_count
points = wp.empty(dtype=wp.vec3, shape=(n_streamlines, point_count))
speed = wp.empty(dtype=float, shape=(n_streamlines, point_count))
fem.interpolate(
gen_streamlines,
at=fem.Cells(self._geo),
dim=n_streamlines,
fields={"u": self.velocity_field},
values={
"spawn_points": spawn_points,
"point_count": self._streamline_point_count,
"dx": self._streamline_dx,
"pos": points,
"speed": speed,
},
)
self._points = points
self._speed = speed
def render(self):
# self.renderer.add_field("solution", self.pressure_field)
self.plot.add_field("pressure", self.pressure_field)
# self.plot.add_field("velocity", self.velocity_field)
if self.renderer is not None:
streamline_count = self._points.shape[0]
point_count = self._streamline_point_count
vertices = self._points.flatten().numpy()
line_offsets = np.arange(streamline_count) * point_count
indices_beg = np.arange(point_count - 1)[np.newaxis, :] + line_offsets[:, np.newaxis]
indices_end = indices_beg + 1
indices = np.vstack((indices_beg.flatten(), indices_end.flatten())).T.flatten()
colors = self._speed.numpy()[:, :-1].flatten()
colors = [bourke_color_map(0.0, 3.0, c) for c in colors]
self.renderer.begin_frame(0)
self.renderer.render_line_list("streamlines", vertices, indices)
self.renderer.render_line_list("streamlines", vertices, indices, colors)
self.renderer.paused = True
self.renderer.end_frame()
def _generate_incompressible_flow(self):
# Function spaces for velocity and pressure (RT1 / P0)
u_space = fem.make_polynomial_space(
geo=self._geo, element_basis=fem.ElementBasis.RAVIART_THOMAS, degree=1, dtype=wp.vec3
)
p_space = fem.make_polynomial_space(geo=self._geo, degree=0, dtype=float)
self.pressure_field = p_space.make_field()
self.velocity_field = u_space.make_field()
# Boundary condition projector and matrices
inflow_test = fem.make_test(u_space, domain=self._inflow)
inflow_trial = fem.make_trial(u_space, domain=self._inflow)
dirichlet_projector = fem.integrate(
noslip_projector_form, fields={"u": inflow_test, "v": inflow_trial}, assembly="nodal", output_dtype=float
)
freeslip_test = fem.make_test(u_space, domain=self._freeslip)
freeslip_trial = fem.make_trial(u_space, domain=self._freeslip)
dirichlet_projector += fem.integrate(
freeslip_projector_form,
fields={"u": freeslip_test, "v": freeslip_trial},
assembly="nodal",
output_dtype=float,
)
fem.normalize_dirichlet_projector(dirichlet_projector)
# Initialize velocity field with BC
fem.interpolate(inflow_velocity, dest=self.velocity_field, at=self._inflow)
# (Diagonal) mass matrix
rho_test = fem.make_test(u_space)
rho_trial = fem.make_trial(u_space)
inv_mass_matrix = fem.integrate(
mass_form, fields={"u": rho_trial, "v": rho_test}, assembly="nodal", output_dtype=float
)
fem_example_utils.invert_diagonal_bsr_matrix(inv_mass_matrix)
# Assemble divergence operator matrix
p_test = fem.make_test(p_space)
u_trial = fem.make_trial(u_space)
divergence_matrix = fem.integrate(
divergence_form,
fields={"u": u_trial, "psi": p_test},
output_dtype=float,
)
# Solve incompressibility
solve_incompressibility(
divergence_matrix,
dirichlet_projector,
inv_mass_matrix.values,
self.pressure_field.dof_values,
self.velocity_field.dof_values,
quiet=self._quiet,
)
if __name__ == "__main__":
import argparse
wp.set_module_options({"enable_backward": False})
parser = argparse.ArgumentParser(formatter_class=argparse.ArgumentDefaultsHelpFormatter)
parser.add_argument("--device", type=str, default=None, help="Override the default Warp device.")
parser.add_argument("--resolution", type=int, default=8, help="Grid resolution.")
parser.add_argument("--degree", type=int, default=2, help="Polynomial degree of shape functions.")
parser.add_argument("--mesh", choices=("grid", "tet", "hex", "nano"), default="grid", help="Mesh type.")
parser.add_argument(
"--headless",
action="store_true",
help="Run in headless mode, suppressing the opening of any graphical windows.",
)
parser.add_argument("--quiet", action="store_true", help="Suppresses the printing out of iteration residuals.")
args = parser.parse_known_args()[0]
with wp.ScopedDevice(args.device):
example = Example(
quiet=args.quiet, degree=args.degree, resolution=args.resolution, mesh=args.mesh, headless=args.headless
)
example.step()
example.render()