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name: physics-and-simulation description: "Route direct PDE, fluid, particle, and SPH simulation workflows built on phi.physics." metadata: disco-role: operating disable-model-invocation: true license: MIT

Physics and Simulation

Use this sub-skill when the task is to run or modify direct simulation code with phi.physics: grid advection, diffusion, incompressible pressure projection, obstacles, particle/grid FLIP or PIC coupling, wave-equation stepping, SPH kernels, finite-volume mesh terms, higher-order fluid stepping, or legacy Domain / boundary behavior.

Route here for

• Advection: advect.semi_lagrangian(), advect.mac_cormack(), advect.advect(), advect.points(), advect.rk4(), advect.finite_rk4(), and advect.differential() / advect.finite_difference().
• Diffusion: diffuse.explicit(), diffuse.implicit(), diffuse.fourier(), diffuse.differential() / diffuse.finite_difference().
• Incompressible flow: fluid.make_incompressible(), fluid.Obstacle, fluid.apply_boundary_conditions(), fluid.boundary_push(), and fluid.incompressible_rk4().
• Particles and SPH: FLIP/PIC particle-grid transfer patterns, boundary push after point advection, sph.neighbor_graph(), sph.evaluate_kernel(), and SPH kernel forces.
• Waves: wave.step(), wave.euler_step(), wave.differential(), and the bundled deterministic wave smoke helper.
• Boundaries: modern grid boundary / extrapolation arguments, per-side extrapolations, Obstacle geometries, active masks, and deprecated Domain notes.
• Higher-order and FVM: direct PDE terms, orders 4/6 where supported, fluid.incompressible_rk4(), mesh Field boundary dictionaries, and finite-volume diffuse.differential() / advect.differential().

Do not route optimization-through-gradients, plotting/UI, visualization-only notebooks, or maintainer-only topology-optimization demos here.

Start with these imports

from phi.flow import *
from phi import field, math
from phi.physics import advect, diffuse, fluid, wave, sph
from phiml.math import extrapolation, Solve, batch, channel, dual, instance, tensor, vec

Use the phi.flow import for common CenteredGrid, StaggeredGrid, PointCloud, Box, Sphere, Cuboid, Obstacle, Noise, resample, and math helpers. Import wave and sph explicitly; they are not part of the short fluid import trio.

Most common decisions

1. Grid fluid step: create a StaggeredGrid velocity, optionally a marker CenteredGrid, then do advection -> diffusion -> projection. Prefer Solve(x0=pressure) in loops to reuse the pressure guess.
2. Advection scheme: use semi_lagrangian for robust defaults; use mac_cormack when numerical diffusion is the main issue and bounded correction is acceptable; use advect.points(..., integrator=advect.finite_rk4) for particle positions sampled from grids.
3. Diffusion scheme: use explicit(..., substeps=N) only when the diffusion CFL is safe; use implicit() for larger dt or viscosity; use fourier() only for periodic grids with constant diffusivity.
4. Obstacle handling: pass Geometry or fluid.Obstacle objects to make_incompressible(); use moving Obstacle(..., velocity=..., angular_velocity=...) to impose obstacle velocities. Higher-order pressure projection does not support obstacles.
5. FLIP/PIC: transfer particles to a grid, project with active=occupied, then update particles with either a FLIP delta (particles += resample(grid_v - prev_grid_v, to=particles)) or PIC replacement, advect points, and call boundary_push().
6. SPH: build a particle Geometry, call sph.neighbor_graph(nodes, kernel, ...), sum edge kernel values over dual, then integrate velocities and positions in your own step function.
7. Waves: use wave.step(u, u_prev, c, dt) for leapfrog state pairs or wave.euler_step(u, v, c, dt) when initial velocity is known. Keep dt small relative to grid spacing and wave speed.
8. Legacy code: replace deprecated Domain(...) helpers with direct constructor dictionaries when possible, e.g. domain = dict(x=64, y=64, bounds=Box(x=1, y=1), extrapolation=extrapolation.PERIODIC).

Verified signatures to rely on

• advect.semi_lagrangian(field, velocity, dt, integrator=advect.euler)
• fluid.make_incompressible(velocity, obstacles=(), solve=Solve(), active=None, order=2, correct_skew=False, wide_stencil=None)
• wave.step(u, u_prev, c=1., dt=1., source=None) and wave.euler_step(u, v, c=1., dt=1., source=None)
• diffuse.explicit(u, diffusivity, dt, substeps=1, order=2, ...), diffuse.implicit(field, diffusivity, dt, solve=Solve('CG'), ...), diffuse.fourier(field, diffusivity, dt)
• sph.neighbor_graph(nodes, kernel, boundary=None, desired_neighbors=None, compute='kernel,grad', format='sparse', search_method='auto', domain=None, periodic=False)

Bundled references and helper

• Detailed recipes: references/workflows.md
• Failure handling: references/troubleshooting.md
• Deterministic wave smoke: scripts/wave_smoke.py

From this sub-skill directory, smoke-test wave stepping with:

python scripts/wave_smoke.py --resolution 32 --steps 24 --dt 0.002

The helper intentionally uses a small grid and far fewer steps than the source demo so it is safe as an installation/API smoke test rather than a benchmark.