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 map_velocity_to_particles(previous_particle_velocity: PointCloud,
velocity_grid: Grid,
occupation_mask: Grid,
previous_velocity_grid: Grid = None,
viscosity: float = 0.) -> PointCloud:
"""
Maps result of velocity projection on grid back to particles.
Provides option to choose between FLIP (particle velocities are updated by the change between projected and initial grid velocities)
and PIC (particle velocities are replaced by the the projected velocities)
method depending on the value of the `initial_v_field`.
Args:
previous_particle_velocity: PointCloud with particle positions as elements and their corresponding velocities as values
velocity_grid: Divergence-free velocity grid
occupation_mask: Binary Grid (same type as `velocity_grid`) indicating which cells hold particles
previous_velocity_grid: Velocity field before projection and force update
viscosity: If previous_velocity_grid is None, the particle-in-cell method (PIC) is applied.
Otherwise this is the ratio between FLIP and PIC (0. for pure FLIP)
Returns:
PointCloud with particle positions as elements and updated particle velocities as values.
"""
viscosity = min(max(0., viscosity), 1.)
if previous_velocity_grid is None:
viscosity = 1.
velocities = math.zeros_like(previous_particle_velocity.values)
if viscosity > 0.:
# --- PIC ---
velocity_grid, _ = extrapolate_valid(velocity_grid, occupation_mask)
velocities += viscosity * (velocity_grid @ previous_particle_velocity).values
if viscosity < 1.:
# --- FLIP ---
v_change_field = velocity_grid - previous_velocity_grid
v_change_field, _ = extrapolate_valid(v_change_field, occupation_mask)
v_change = (v_change_field @ previous_particle_velocity).values
velocities += (1 - viscosity) * (previous_particle_velocity.values + v_change)
return previous_particle_velocity.with_values(velocities)