CFL Number & CFD Time Step Calculator

Transient CFD & numerical hyperbolic solvers: Determine the Courant-Friedrichs-Lewy (CFL) stability number, convective/acoustic wave speeds, and maximum permissible time step ($Delta t$).

Grid Scale & Flow Velocity

Minimum Cell Size Δx (mm): Smallest grid cell dimension

Fluid Convective Velocity u (m/s): Peak flow velocity magnitude

Speed of Sound c (m/s): Air = 343 m/s (Set 0 for Incompressible)

Target CFL Number: Explicit ≤ 1.0, Implicit 2 - 50

Solver Time Scheme: Numerical time integration

Spatial Dimension: Multidimensional stability

Time Step & Wave Speed Results

Allowable Time Step (Δt)

Governing Wave Speed (a_wave)

Cell Transit Duration (t_cell)

Δx / u_convective

Iteration Frequency

1 / Δt iterations/sec

Dimensional Scaling Factor

1 / N_dim restriction

Time Steps per 1s Physical Flow

Computational workload

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Frequently Asked Questions

Why does the acoustic wave speed restrict the time step so drastically in low-speed compressible flows?

In low-Mach compressible simulations (e.g., M = 0.05), air flows at 17 m/s while sound travels at 340 m/s. The explicit CFL condition is dictated by acoustic wave speed (340 + 17 = 357 m/s), forcing a time step 20 times smaller than needed to resolve the fluid convection alone.

What is the physical interpretation of CFL = 1?

A CFL of 1 means that fluid particles (or acoustic wavefronts) travel exactly the distance of one cell width (Δx) in one discrete time step (Δt).

How does grid refinement impact simulation runtime?

Halving the cell size (Δx / 2) in a 3D explicit simulation increases cell count by 8× (2³) and cuts the maximum stable time step in half (Δt / 2), increasing total computing workload by 16× (2⁴).