Description
Return one face's finite-volume Courant contribution.
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 face's finite-volume Courant contribution.
When to use this tool
Use Finite Volume Courant One Face Term when checking the stated local stability, diffusion or sampling convention.
How to use the tool and how it works
- Enter normalSpeed, faceArea, cellVolume, step. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read courantContribution. Use the output convention below.
Return one face's finite-volume Courant contribution. Require faceArea/step >= 0 and cellVolume > 0; contribution = abs(normalSpeed)*faceArea*step/cellVolume.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| normalSpeed | Normal Speed | Required. Finite number. |
| faceArea | Face Area | Required. Finite number; minimum 0. |
| cellVolume | Cell Volume | Required. Finite number; strictly above 0. |
| step | Step duration or increment under the stated convention. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| courantContribution | Courant Contribution | Required. Finite number. |
{
"input": {
"normalSpeed": 2,
"faceArea": 3,
"cellVolume": 6,
"step": 0.5
},
"output": {
"courantContribution": 0.5
}
}Limitations and assumptions
- Normal speed and face/cell geometry are supplied; one contribution is not the whole-cell sum or a complete stability condition.
- 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 Courant Component
Return one signed Courant number and magnitude.
- Grid Diffusion Stability Ratio
Return a grid diffusion number and explicit-Euler limit ratio.