Description
Return a grid diffusion number and explicit-Euler limit ratio.
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 grid diffusion number and explicit-Euler limit ratio.
When to use this tool
Use Grid Diffusion Stability Ratio when checking the stated local stability, diffusion or sampling convention.
How to use the tool and how it works
- Enter diffusivity, timeStep, gridWidth, dimensions. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read fourierNumber, explicitEulerRatio. Use the output convention below.
Return a grid diffusion number and explicit-Euler limit ratio. Require diffusivity/timeStep >= 0, gridWidth > 0 and dimensions 1..3; Fourier number = diffusivity*dt/h², explicitEulerRatio = 2*d*Fourier.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| diffusivity | Diffusivity | Required. Finite number; minimum 0. |
| timeStep | Step duration in the same time unit used by rates and accelerations. | Required. Finite number; minimum 0. |
| gridWidth | Grid Width | Required. Finite number; strictly above 0. |
| dimensions | Dimensions | Required. Safe integer; minimum 1; maximum 3. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| fourierNumber | Fourier Number | Required. Finite number. |
| explicitEulerRatio | Explicit Euler Ratio | Required. Finite number. |
{
"input": {
"diffusivity": 1,
"timeStep": 0.1,
"gridWidth": 1,
"dimensions": 2
},
"output": {
"fourierNumber": 0.1,
"explicitEulerRatio": 0.4
}
}Limitations and assumptions
- The standard equal-spacing local ratio is not itself a guarantee for arbitrary operators, boundaries or time integrators.
- 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.
- Mesh Refinement Ratio CFL Scaling
Scale a time step under a supplied refinement law.