LBM BGK Stability Map

Compute BGK tau, omega, and lattice Mach from physical scaling and visualize the safe operating window.

visual calculatorNumerics & Stability

Read the flow shape before trusting the number.

This page turns a CFD setup into regime, scale, and dominant-effect cues. Adjust the calculator below and compare the moving graphic with the computed result.

input scale

model

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LBMBGKlattice Machstability

formula

KaTeX rendered

\begin{aligned}\text{nu\_lu = nu\_phys dt/dx\^{}2}\\[0.35em]\text{tau = 0.5 + nu\_lu / c\_s\^{}2}\\[0.35em]\text{Ma\_lu = U\_lu / c\_s}\end{aligned}

ASCII source

nu_lu = nu_phys dt/dx^2, tau = 0.5 + nu_lu / c_s^2, Ma_lu = U_lu / c_s

U physical (m/s)L physical (m)nu physical (m^2/s)cells across LU lattice

tau

0.5004

omega

1.9985

lattice Mach

0.1386

nu lattice

0.0001

dx (m)

0.0006

dt (s)

5.000e-5

Re physical

1.000e+5

status

tau near unstable range

For weakly compressible LBM, keep lattice Mach small and tau safely above 0.5. Practical limits depend on collision model and boundary treatment.

LBM BGK lattice Mach stability