def accessible_mask(
self,
not_accessible: tuple or list,
type: type = CenteredGrid) -> CenteredGrid or StaggeredGrid:
"""
Unifies domain and Obstacle or Geometry objects into a binary StaggeredGrid mask which can be used
to enforce boundary conditions.
Args:
not_accessible: blocked region(s) of space specified by geometries
Returns:
Binary mask indicating valid fields w.r.t. the boundary conditions.
The result is of type `type` and uses the extrapolation `Domain.boundaries['accessible_extrapolation']`.
"""
accessible_mask = self.scalar_grid(
HardGeometryMask(~union(not_accessible)),
extrapolation=self.boundaries['accessible_extrapolation'])
if type is CenteredGrid:
return accessible_mask
elif type is StaggeredGrid:
return field.stagger(accessible_mask, math.minimum,
self.boundaries['accessible_extrapolation'])
else:
raise ValueError('Unknown grid type: %s' % type)
def accessible_mask(self, not_accessible: tuple or list, type: type = CenteredGrid, extrapolation='accessible') -> CenteredGrid or StaggeredGrid:
"""
Unifies domain and Obstacle or Geometry objects into a binary StaggeredGrid mask which can be used
to enforce boundary conditions.
Args:
not_accessible: blocked region(s) of space specified by geometries
type: class of Grid to create, must be either CenteredGrid or StaggeredGrid
extrapolation: (optional) grid extrapolation, defaults to Domain.boundaries['accessible']
Returns:
Binary mask indicating valid fields w.r.t. the boundary conditions.
"""
extrapolation = extrapolation if isinstance(extrapolation, math.Extrapolation) else self.boundaries[extrapolation]
accessible_mask = self.scalar_grid(HardGeometryMask(~union(not_accessible)), extrapolation=extrapolation)
if type is CenteredGrid:
return accessible_mask
elif type is StaggeredGrid:
return field.stagger(accessible_mask, math.minimum, extrapolation)
else:
raise ValueError('Unknown grid type: %s' % type)
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