CFL & Diffusion Stability Calculator
Screen a spatial grid and time step against common linear stability limits. Choose first-order upwind advection, the standard explicit wave scheme or FTCS heat diffusion and calculate the relevant dimensionless number and maximum time step.
How this tool works
Advection and wave use C=|v|Δt/Δx or cΔt/Δx with a common limit C≤1. One-dimensional FTCS diffusion uses r=αΔt/Δx² with the standard limit r≤1/2.
Example
With Δx=0.01, advection speed 1 and Δt=0.005, the CFL number is 0.5 and passes the usual upwind stability screen.
Common questions
Does passing CFL guarantee an accurate result?
No. Stability only means numerical errors should not grow without bound under the assumptions of the criterion. Accuracy can require much finer resolution.
Do all schemes use the same CFL limit?
No. Stability regions depend on the spatial discretization and time integrator. This calculator states the specific common scheme assumed for each test.