Description
Scale a time step under a supplied refinement law.
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.
Scale a time step under a supplied refinement law.
When to use this tool
Use Mesh Refinement Ratio CFL Scaling when checking the stated local stability, diffusion or sampling convention.
How to use the tool and how it works
- Enter oldStep, refinementRatio, spatialPower. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read newStep, stepRatio. Use the output convention below.
Scale a time step under a supplied refinement law. Require oldStep >= 0, refinementRatio >= 1 and spatialPower > 0; stepRatio = refinementRatio^-power, newStep = oldStep*ratio.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| oldStep | Old Step | Required. Finite number; minimum 0. |
| refinementRatio | Refinement Ratio | Required. Finite number; minimum 1. |
| spatialPower | Spatial Power | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| newStep | New Step | Required. Finite number. |
| stepRatio | Step Ratio | Required. Finite number. |
{
"input": {
"oldStep": 1,
"refinementRatio": 2,
"spatialPower": 1
},
"output": {
"newStep": 0.5,
"stepRatio": 0.5
}
}Limitations and assumptions
- The power is caller-selected, such as one for an advective scaling or two for diffusion; actual stability is not assessed.
- 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.
- CFL Diagonal Grid Step Budget
Compare a summed grid Courant number with a supplied limit.