JAX-accelerated dimensionless groups for scaling Physics AI models. Inputs may have leading batch dimensions; all operations broadcast. All methods are @jax.jit.
Fluid flow
Groups.re(u, L, rho, mu)
Reynolds number: ρ u L / μ
Ratio of inertial to viscous forces.
u [m/s], L [m], rho [kg/m³], mu [Pa·s] → Re (dimensionless).
SciML: scales the diffusive term in Navier-Stokes loss.
Groups.ma(u, a)
Mach number: u / a
Flow velocity to speed of sound.
u [m/s], a [m/s] → Ma (dimensionless).
Groups.we(rho, u, L, sigma)
Weber number
Inertia to surface tension. rho [kg/m³], u [m/s], L [m], sigma [N/m].
Groups.eu(dp, rho, u)
Euler number
Pressure to inertial forces. dp [Pa], rho [kg/m³], u [m/s]. Valves, orifices, pumps.
Groups.st(f, u, L)
Strouhal number
Oscillatory to inertial. f [Hz], u [m/s], L [m]. Vortex shedding, unsteady aerodynamics.
Groups.ca(mu, u, sigma)
Capillary number
Viscous to surface tension. Porous media, thin-film coating.
Groups.bo(rho, g, L, sigma)
Bond number
Gravity to surface tension. Bubbles, capillary action, microfluidics.
Heat transfer
Groups.pr(mu, cp, k)
Prandtl number: cp μ / k
Momentum to thermal diffusivity. mu [Pa·s], cp [J/(kg·K)], k [W/(m·K)].
SciML: bridges velocity and temperature in multi-physics PINNs.
Groups.nu(h, L, k)
Nusselt number: h L / k
Convective to conductive heat transfer. h [W/(m²·K)], L [m], k [W/(m·K)].
Groups.gr(beta, dT, L, nu)
Grashof number
Buoyancy to viscous. beta [1/K], dT [K], L [m], nu [m²/s]. Natural convection.
Groups.bi(h, L, k_solid)
Biot number
Internal vs external thermal resistance. Transient conduction, lumped mass.
Groups.fo(alpha, t, L)
Fourier number
Dimensionless time for heat conduction. alpha [m²/s], t [s], L [m].
Groups.ec(u, cp, dT)
Eckert number
Kinetic energy vs enthalpy difference. Viscous dissipation heating.
Transport and composition
Groups.pe(re, pr)
Péclet number: Re × Pr
Advection to diffusion. Heat/mass transfer in flowing fluids.
Groups.sc(nu, D)
Schmidt number
Momentum to mass diffusivity. nu [m²/s], D [m²/s]. Mass transfer, CVD.
Groups.le(sc, pr)
Lewis number: Sc / Pr
Thermal to mass diffusivity. Combined heat and mass transfer, combustion.
Groups.fo_mass(D, t, L)
Fourier number for mass: D t / L²
Dimensionless time for mass diffusion. D [m²/s], t [s], L [m]. Fick diffusion, species PINNs.
Groups.pe_mass(re, sc)
Péclet for species: Re × Sc
Advection to mass diffusion. Use with Laws.advection_diffusion for mass transfer.
Waves
Groups.wavenumber(k, L)
Dimensionless wavenumber: k L
k [1/m], L [m]. Helmholtz equation, frequency-domain wave scaling.
Groups.st_wave(omega, L, c)
Wave Strouhal: ω L / c
omega [rad/s], L [m], c [m/s]. Wave equation, acoustics, resonance.
Porous media and rarefaction
Groups.da(K, L)
Darcy number
Permeability to characteristic area. K [m²], L [m]. Porous-media-informed networks.
Groups.kn(lambda_mfp, L)
Knudsen number
Mean free path to length scale. Rarefied gas dynamics; when Navier-Stokes breaks down.