Description
Return a diffusion stencil's center weight and negative flag.
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 a diffusion stencil's center weight and negative flag.
When to use this tool
Use Heat Stencil Negative Weight Flag when checking the stated local stability, diffusion or sampling convention.
How to use the tool and how it works
- Enter diffusionNumber, dimensions. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read centerWeight, negativeCenter. Inspect negativeCenter before interpreting the associated values.
Return a diffusion stencil's center weight and negative flag. Require diffusionNumber >= 0 and whole dimensions >= 1; centerWeight = 1-2*dimensions*diffusionNumber, negativeCenter tests weight < 0.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| diffusionNumber | Diffusion Number | Required. Finite number; minimum 0. |
| dimensions | Dimensions | Required. Safe integer; minimum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| centerWeight | Center Weight | Required. Finite number. |
| negativeCenter | True only below zero; zero centerWeight is not flagged negative. | Required. Boolean. |
{
"input": {
"diffusionNumber": 0.2,
"dimensions": 2
},
"output": {
"centerWeight": 0.19999999999999996,
"negativeCenter": false
}
}Limitations and assumptions
- Zero weight is not negative; this local monotonicity condition is not a complete stability or accuracy analysis.
- 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.
- Grid Courant Component
Return one signed Courant number and magnitude.