def _test_make_incompressible(self, grid_type: type,
extrapolation: math.Extrapolation,
**batch_dims):
result = None
for i, backend in enumerate(BACKENDS):
with backend:
smoke = CenteredGrid(Sphere(
center=(math.random_uniform(batch(**batch_dims)) * 100,
10),
radius=5),
extrapolation,
x=16,
y=20,
bounds=Box[0:100, 0:100])
velocity = grid_type(0,
extrapolation,
x=16,
y=20,
bounds=Box[0:100, 0:100])
for _ in range(2):
velocity += smoke * (0, 0.1) @ velocity
velocity, _ = fluid.make_incompressible(velocity)
math.assert_close(divergence(velocity).values,
0,
abs_tolerance=2e-5)
if result is None:
result = velocity
else:
field.assert_close(
result,
abs_tolerance=1e-5,
msg=
f"Simulation with {backend} does not match {BACKENDS[:i]}"
)
def laplace(p):
grad = gradient(p, type(velocity))
grad *= hard_bcs
grad = grad.with_(
extrapolation=domain.boundaries['near_vector_extrapolation'])
div = divergence(grad)
lap = where(active, div, p)
return lap
def make_incompressible(velocity: StaggeredGrid,
domain: Domain,
particles: PointCloud,
obstacles: tuple or list or StaggeredGrid = (),
solve=math.Solve('auto', 1e-5, 0, gradient_solve=math.Solve('auto', 1e-5, 1e-5))):
"""
Projects the given velocity field by solving for the pressure and subtracting its spatial_gradient.
Args:
velocity: Current velocity field as StaggeredGrid
domain: Domain object
particles: `PointCloud` holding the current positions of the particles
obstacles: Sequence of `phi.physics.Obstacle` objects or binary StaggeredGrid marking through-flow cell faces
solve: Parameters for the pressure solve_linear
Returns:
velocity: divergence-free velocity of type `type(velocity)`
pressure: solved pressure field, `CenteredGrid`
iterations: Number of iterations required to solve_linear for the pressure
divergence: divergence field of input velocity, `CenteredGrid`
occupation_mask: StaggeredGrid
"""
points = particles.with_values(math.tensor(1., convert=True))
occupied_centered = points @ domain.scalar_grid()
occupied_staggered = points @ domain.staggered_grid()
if isinstance(obstacles, StaggeredGrid):
accessible = obstacles
else:
accessible = domain.accessible_mask(union(*[obstacle.geometry for obstacle in obstacles]), type=StaggeredGrid)
# --- Extrapolation is needed to exclude border divergence from the `occupied_centered` mask and thus
# from the pressure solve_linear. If particles are randomly distributed, the `occupied_centered` mask
# could sometimes include the divergence at the borders (due to single particles right at the edge
# which temporarily deform the `occupied_centered` mask when moving into a new cell). This would then
# get compensated by the pressure. This is unwanted for falling liquids and therefore prevented by this
# extrapolation. ---
velocity_field, _ = extrapolate_valid(velocity * occupied_staggered, occupied_staggered, 1)
velocity_field *= accessible # Enforces boundary conditions after extrapolation
div = field.divergence(velocity_field) * occupied_centered # Multiplication with `occupied_centered` excludes border divergence from pressure solve_linear
@field.jit_compile_linear
def matrix_eq(p):
return field.where(occupied_centered, field.divergence(field.spatial_gradient(p, type=StaggeredGrid) * accessible), p)
if solve.x0 is None:
solve = copy_with(solve, x0=domain.scalar_grid())
pressure = field.solve_linear(matrix_eq, div, solve)
def pressure_backward(_p, _p_, dp):
return dp * occupied_centered.values,
add_mask_in_gradient = math.custom_gradient(lambda p: p, pressure_backward)
pressure = pressure.with_values(add_mask_in_gradient(pressure.values))
gradp = field.spatial_gradient(pressure, type=type(velocity_field)) * accessible
return velocity_field - gradp, pressure, occupied_staggered
def masked_laplace(pressure: CenteredGrid, hard_bcs: Grid,
active: CenteredGrid):
grad = spatial_gradient(pressure,
hard_bcs.extrapolation,
type=type(hard_bcs))
grad *= hard_bcs
div = divergence(grad)
lap = where(active, div, pressure)
return lap
def _test_make_incompressible_batched(self, grid_type):
DOMAIN = Domain(x=16, y=16, boundaries=CLOSED, bounds=Box[0:100, 0:100])
smoke = DOMAIN.scalar_grid(Sphere(center=(math.random_uniform(batch=2) * 100, 10), radius=5))
velocity = DOMAIN.vector_grid(0, grid_type)
for _ in range(2):
velocity += smoke * (0, 0.1) >> velocity
velocity, pressure, _, _ = fluid.make_incompressible(velocity, DOMAIN)
math.assert_close(divergence(velocity).values, 0, abs_tolerance=2e-5)
return velocity.values
def step(self,
fluid,
dt=1.0,
obstacles=(),
gravity=Gravity(),
density_effects=(),
velocity_effects=()):
# pylint: disable-msg = arguments-differ
gravity = gravity_tensor(gravity, fluid.rank)
velocity = fluid.velocity
density = fluid.density
result: SolveInfo = None
div = field.divergence(velocity)
if self.make_input_divfree:
velocity, result = make_incompressible(velocity, obstacles)
# --- Advection ---
density = advect.semi_lagrangian(density, velocity, dt=dt)
velocity = advected_velocity = advect.semi_lagrangian(velocity,
velocity,
dt=dt)
if self.conserve_density and fluid.domain.boundaries[
'accessible'] == math.extrapolation.ZERO: # solid boundary
density = field.normalize(density, fluid.density)
# --- Effects ---
for effect in density_effects:
density = effect_applied(effect, density, dt)
for effect in velocity_effects:
velocity = effect_applied(effect, velocity, dt)
velocity += (density * -gravity * fluid.buoyancy_factor *
dt).at(velocity)
divergent_velocity = velocity
# --- Pressure solve_linear ---
if self.make_output_divfree:
velocity, result = make_incompressible(velocity, obstacles)
solve_info = {
'pressure': result.x,
'iterations': result.iterations,
'divergence': div,
'advected_velocity': advected_velocity,
'divergent_velocity': divergent_velocity,
}
return fluid.copied_with(density=density,
velocity=velocity,
age=fluid.age + dt,
solve_info=solve_info)
def matrix_eq(p):
return field.where(occupied_centered, field.divergence(field.spatial_gradient(p, type=StaggeredGrid) * accessible), p)
def test_divergence_centered(self):
v = CenteredGrid(1, extrapolation.ZERO, bounds=Box[0:1, 0:1], x=3,
y=3) * (1, 0) # flow to the right
div = field.divergence(v).values
math.assert_close(div.y[0], (1.5, 0, -1.5))
def make_incompressible(velocity: Grid,
domain: Domain,
obstacles: tuple or list = (),
solve_params: math.LinearSolve = math.LinearSolve(
None, 1e-3),
pressure_guess: CenteredGrid = None):
"""
Projects the given velocity field by solving for the pressure and subtracting its gradient.
This method is similar to :func:`field.divergence_free()` but differs in how the boundary conditions are specified.
Args:
velocity: Vector field sampled on a grid
domain: Used to specify boundary conditions
obstacles: List of Obstacles to specify boundary conditions inside the domain (Default value = ())
pressure_guess: Initial guess for the pressure solve
solve_params: Parameters for the pressure solve
Returns:
velocity: divergence-free velocity of type `type(velocity)`
pressure: solved pressure field, `CenteredGrid`
iterations: Number of iterations required to solve for the pressure
divergence: divergence field of input velocity, `CenteredGrid`
"""
input_velocity = velocity
active = domain.grid(
HardGeometryMask(~union(*[obstacle.geometry
for obstacle in obstacles])),
extrapolation=domain.boundaries['active_extrapolation'])
accessible = domain.grid(
active, extrapolation=domain.boundaries['accessible_extrapolation'])
hard_bcs = field.stagger(accessible,
math.minimum,
domain.boundaries['accessible_extrapolation'],
type=type(velocity))
velocity = layer_obstacle_velocities(velocity * hard_bcs, obstacles).with_(
extrapolation=domain.boundaries['near_vector_extrapolation'])
div = divergence(velocity)
if domain.boundaries[
'near_vector_extrapolation'] == math.extrapolation.BOUNDARY:
div -= field.mean(div)
# Solve pressure
def laplace(p):
grad = gradient(p, type(velocity))
grad *= hard_bcs
grad = grad.with_(
extrapolation=domain.boundaries['near_vector_extrapolation'])
div = divergence(grad)
lap = where(active, div, p)
return lap
pressure_guess = pressure_guess if pressure_guess is not None else domain.scalar_grid(
0)
converged, pressure, iterations = field.solve(laplace,
y=div,
x0=pressure_guess,
solve_params=solve_params,
constants=[active, hard_bcs])
if math.all_available(converged) and not math.all(converged):
raise AssertionError(
f"pressure solve did not converge after {iterations} iterations\nResult: {pressure.values}"
)
# Subtract grad pressure
gradp = field.gradient(pressure, type=type(velocity)) * hard_bcs
velocity = (velocity -
gradp).with_(extrapolation=input_velocity.extrapolation)
return velocity, pressure, iterations, div
def make_incompressible(
velocity: GridType,
obstacles: tuple or list = (),
solve=math.Solve('auto',
1e-5,
1e-5,
gradient_solve=math.Solve('auto', 1e-5, 1e-5))
) -> Tuple[GridType, CenteredGrid]:
"""
Projects the given velocity field by solving for the pressure and subtracting its spatial_gradient.
This method is similar to :func:`field.divergence_free()` but differs in how the boundary conditions are specified.
Args:
velocity: Vector field sampled on a grid
obstacles: List of Obstacles to specify boundary conditions inside the domain (Default value = ())
solve: Parameters for the pressure solve as.
Returns:
velocity: divergence-free velocity of type `type(velocity)`
pressure: solved pressure field, `CenteredGrid`
"""
assert isinstance(
obstacles,
(tuple,
list)), f"obstacles must be a tuple or list but got {type(obstacles)}"
input_velocity = velocity
accessible_extrapolation = _accessible_extrapolation(
input_velocity.extrapolation)
active = CenteredGrid(
HardGeometryMask(~union(*[obstacle.geometry
for obstacle in obstacles])),
resolution=velocity.resolution,
bounds=velocity.bounds,
extrapolation=extrapolation.NONE)
accessible = active.with_extrapolation(accessible_extrapolation)
hard_bcs = field.stagger(accessible,
math.minimum,
input_velocity.extrapolation,
type=type(velocity))
velocity = apply_boundary_conditions(velocity, obstacles)
div = divergence(velocity) * active
if not input_velocity.extrapolation.connects_to_outside:
assert solve.preprocess_y is None, "fluid.make_incompressible() does not support custom preprocessing"
solve = copy_with(solve,
preprocess_y=_balance_divergence,
preprocess_y_args=(active, ))
if solve.x0 is None:
pressure_extrapolation = _pressure_extrapolation(
input_velocity.extrapolation)
solve = copy_with(solve,
x0=CenteredGrid(
0,
resolution=div.resolution,
bounds=div.bounds,
extrapolation=pressure_extrapolation))
pressure = math.solve_linear(masked_laplace,
f_args=[hard_bcs, active],
y=div,
solve=solve)
grad_pressure = field.spatial_gradient(
pressure, input_velocity.extrapolation, type=type(velocity)) * hard_bcs
velocity = velocity - grad_pressure
return velocity, pressure
def test_divergence_centered(self):
v = field.CenteredGrid(math.ones(x=3, y=3), Box[0:1, 0:1],
math.extrapolation.ZERO) * (
1, 0) # flow to the right
div = field.divergence(v).values
math.assert_close(div.y[0], (1.5, 0, -1.5))
def make_incompressible(
velocity: StaggeredGrid,
domain: Domain,
obstacles: tuple or list or StaggeredGrid = (),
particles: PointCloud or None = None,
solve_params: math.LinearSolve = math.LinearSolve(),
pressure_guess: CenteredGrid = None
) -> Tuple[StaggeredGrid, CenteredGrid, math.Tensor, CenteredGrid,
StaggeredGrid]:
"""
Projects the given velocity field by solving for the pressure and subtracting its spatial_gradient.
Args:
velocity: Current velocity field as StaggeredGrid
obstacles: Sequence of `phi.physics.Obstacle` objects or binary StaggeredGrid marking through-flow cell faces
particles (Optional if occupation masks are provided): Pointcloud holding the current positions of the particles
domain (Optional if occupation masks are provided): Domain object
pressure_guess (Optional): Initial pressure guess as CenteredGrid
solve_params: Parameters for the pressure solve
Returns:
velocity: divergence-free velocity of type `type(velocity)`
pressure: solved pressure field, `CenteredGrid`
iterations: Number of iterations required to solve for the pressure
divergence: divergence field of input velocity, `CenteredGrid`
occupation_mask: StaggeredGrid
"""
points = particles.with_(values=math.wrap(1))
occupied_centered = points >> domain.grid()
occupied_staggered = points >> domain.staggered_grid()
if isinstance(obstacles, StaggeredGrid):
accessible = obstacles
else:
accessible = domain.accessible_mask(
union(*[obstacle.geometry for obstacle in obstacles]),
type=StaggeredGrid)
# --- Extrapolation is needed to exclude border divergence from the `occupied_centered` mask and thus
# from the pressure solve. If particles are randomly distributed, the `occupied_centered` mask
# could sometimes include the divergence at the borders (due to single particles right at the edge
# which temporarily deform the `occupied_centered` mask when moving into a new cell) which would then
# get compensated by the pressure. This is unwanted for falling liquids and therefore prevented by this
# extrapolation. ---
velocity_field, _ = extrapolate_valid(velocity * occupied_staggered,
occupied_staggered, 1)
velocity_field *= accessible # Enforces boundary conditions after extrapolation
div = field.divergence(
velocity_field
) * occupied_centered # Multiplication with `occupied_centered` excludes border divergence from pressure solve
def matrix_eq(p):
return field.where(
occupied_centered,
field.divergence(
field.spatial_gradient(p, type=StaggeredGrid) * accessible), p)
converged, pressure, iterations = field.solve(matrix_eq,
div,
pressure_guess
or domain.grid(),
solve_params=solve_params)
gradp = field.spatial_gradient(pressure,
type=type(velocity_field)) * accessible
return velocity_field - gradp, pressure, iterations, div, occupied_staggered