Diffusion Time-Step Limit

Compute stability limits and maximum time step for explicit diffusion updates.

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

check

diffusionstabilityheat equation

formula

KaTeX rendered

\begin{aligned}\text{Fo = alpha dt / dx\^{}2}\\[0.35em]\text{dt\_max = Fo\_max dx\^{}2 / alpha}\end{aligned}

ASCII source

Fo = alpha dt / dx^2, dt_max = Fo_max dx^2 / alpha

alpha (m^2/s)dt (s)dx (m)spatial dimension

1.000e-4

Fo_max

0.5000

dt_max (s)

5.0000

For central explicit diffusion, the stability limit tightens with dimension. Non-uniform grids and anisotropy can make the real limit stricter.

diffusion stability heat equation