Description
Calculate signed and absolute single-axis supplied Courant numbers.
Numerical physics calculations depend on discretization, index conventions, boundary conditions and model units. A local force kick is only part of an integration method, a stencil residual is not a solved field, and a one-sided power weight is not a spectral-density normalization. Floating-point resolution also limits grid and coordinate representations.
Calculate signed and absolute single-axis supplied Courant numbers.
When to use this tool
Use Courant Number Single Axis when you already have signedSpeed, timeStep, cellWidth and need to calculate signed and absolute single-axis supplied Courant numbers.
How to use the tool and how it works
- Enter signedSpeed, timeStep, cellWidth. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read signedCourantNumber, absoluteCourantNumber. Use the output convention below.
Require timeStep>=0 and cellWidth>0; return speed*time/width and abs(speed)*time/width.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| signedSpeed | Signed Speed | Required. Finite number. |
| timeStep | Time Step | Required. Finite number; minimum 0. |
| cellWidth | Cell Width | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| signedCourantNumber | signedSpeed*timeStep/cellWidth; no stability threshold is chosen. | Required. Finite number. |
| absoluteCourantNumber | Absolute Courant Number | Required. Finite number. |
{
"input": {
"signedSpeed": 2,
"timeStep": 0.1,
"cellWidth": 0.5
},
"output": {
"signedCourantNumber": 0.4,
"absoluteCourantNumber": 0.4
}
}Limitations and assumptions
- The speed may be signed. This alone does not enforce a method-specific CFL condition, combine dimensions or establish stability or a suitable time step.
- 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
Use the complete discretized model, integration algorithm and boundary treatment. Assess convergence, conservation and stability with the full calculation; individual residuals, CFL components, relaxation terms and index mappings do not establish numerical accuracy or physical validity.
References
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