Description
Return one signed Courant number and magnitude.
A dimensionless time-step ratio, free-diffusion scale or sampling weight assumes a particular model and data basis. Local bounds and factors can help diagnose a method, but accuracy, stability and statistical uncertainty depend on the complete algorithm and its assumptions.
Return one signed Courant number and magnitude.
When to use this tool
Use Grid Courant Component when checking the stated local stability, diffusion or sampling convention.
How to use the tool and how it works
- Enter velocity, timeStep, spacing. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read signedCourant, magnitude. Use the output convention below.
Return one signed Courant number and magnitude. Require timeStep >= 0 and spacing > 0; signedCourant = velocity*timeStep/spacing, magnitude is its absolute value.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| velocity | Velocity | Required. Finite number. |
| timeStep | Step duration in the same time unit used by rates and accelerations. | Required. Finite number; minimum 0. |
| spacing | Spacing | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| signedCourant | Signed Courant | Required. Finite number. |
| magnitude | Magnitude | Required. Finite number. |
{
"input": {
"velocity": 2,
"timeStep": 0.5,
"spacing": 4
},
"output": {
"signedCourant": 0.25,
"magnitude": 0.25
}
}Limitations and assumptions
- Matching length/time units are required; the tool does not select a scheme-specific stability threshold.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Analyze the full numerical or stochastic method, its support and error behavior before treating a local factor as a reliability guarantee.
References
Similar or alternative tools
- Grid Diffusion Stability Ratio
Return a grid diffusion number and explicit-Euler limit ratio.
- Finite Volume Courant One Face Term
Return one face's finite-volume Courant contribution.