Description
Compare a summed grid Courant number with a supplied limit.
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.
Compare a summed grid Courant number with a supplied limit.
When to use this tool
Use CFL Diagonal Grid Step Budget when checking the stated local stability, diffusion or sampling convention.
How to use the tool and how it works
- Enter speeds, spacings, timeStep, suppliedLimit. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read courantSum, margin. Use the output convention below.
Compare a summed grid Courant number with a supplied limit. Require aligned nonempty speeds/positive spacings, timeStep >= 0 and suppliedLimit >= 0; sum = dt*sum(abs(speed)/spacing), margin = limit-sum.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| speeds | Speeds | Required. Array of finite number; maximum items 256. |
| spacings | Spacings | Required. Array of finite number; maximum items 256. |
| timeStep | Step duration in the same time unit used by rates and accelerations. | Required. Finite number; minimum 0. |
| suppliedLimit | Supplied Limit | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| courantSum | Courant Sum | Required. Finite number. |
| margin | Margin | Required. Finite number. |
{
"input": {
"speeds": [
1,
2
],
"spacings": [
2,
4
],
"timeStep": 0.5,
"suppliedLimit": 1
},
"output": {
"courantSum": 0.5,
"margin": 0.5
}
}Limitations and assumptions
- The limit is supplied; actual numerical stability depends on the full discretization, operator and boundary conditions.
- 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.