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CFL / Courant Number Calculator - Stable Time Step for CFD

Your CFD simulation was running fine — then the residuals exploded to infinity and everything turned to NaN. Nine times out of ten, the culprit is a time step that's too large, violating the CFL condition . The Courant–Friedrichs–Lewy number is the single most important control on the stability of any transient (time-marching) simulation, and getting it right is the difference between a clean run and a wasted afternoon. This guide gives you a free CFL calculator (validated against the standard formulas), explains the condition in plain language, and shows you exactly how to choose a stable, efficient time step. Figure 1. The Courant number measures how far the flow travels per time step relative to the cell size. Keep it below 1 (explicit solvers) and the simulation stays stable; exceed it and the solution diverges. Table of Contents The CFL / Courant Number Calculator What Is the CFL / Courant Number? The CFL Stability Condition The Formula...
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Dimensionless Numbers Calculator (All-in-One) - Reynolds, Nusselt, Prandtl & More

Every equation in fluid mechanics and heat transfer eventually comes down to a handful of magic numbers. Is the flow laminar or turbulent? Does compressibility matter? Will heat move by convection or conduction? Is the flow driven by a pump or by buoyancy? The answers all live in dimensionless numbers — unitless ratios that capture the physics in a single value. This all-in-one calculator computes the ten most important ones — Reynolds, Prandtl, Nusselt, Mach, Froude, Peclet, Grashof, Rayleigh, Weber and Biot — each with its formula, meaning and validated math. Figure 1. Dimensionless numbers each express a ratio of competing physical effects. Together they describe almost any flow or heat-transfer problem — and this tool computes them all in one place. Table of Contents The All-in-One Calculator What Are Dimensionless Numbers? Quick Reference Table Reynolds Number (Re) Prandtl Number (Pr) Nusselt Number (Nu) Mach Number (Ma) ...
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Turbulence Intensity & Length Scale Calculator for CFD Inlet Conditions

You set up a perfect mesh, chose k-ω SST, hit run — and your turbulence quietly dies before the flow even reaches the object. The cause is almost always the same: bad turbulence inlet boundary conditions. Two-equation models like k-ε and k-ω SST need starting values for turbulence at the inlet, but those values ( k , ε , ω ) are hard to guess directly. The trick every CFD engineer uses is to specify two intuitive quantities instead — turbulence intensity (I) and length scale (ℓ) — and convert them. This guide gives you a free, validated calculator that does exactly that, plus the theory behind every number. Figure 1. At a CFD inlet you specify turbulence intensity (I) and length scale (ℓ), and the solver converts them into k, ε and ω — the quantities the turbulence model actually solves. Table of Contents The Turbulence Inlet BC Calculator Why Turbulence Inlet Conditions Matter Turbulence Intensity (I) Turbulence Length Scale (ℓ) The Conv...
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