Description
Compare a centered spatial derivative's mode factor with exact wavenumber.
Numerical grids and sampled modes require explicit coordinate, boundary and sign conventions. A staggered location, minimum-image gap or Nyquist label is one component of a discretization rather than a complete field solve or unique physical interpretation.
Compare a centered spatial derivative's mode factor with exact wavenumber.
When to use this tool
Use Numerical Dispersion One Grid Phase when checking the stated grid-coordinate, periodic-image or sampled-mode convention.
How to use the tool and how it works
- Enter wavenumber, spacing. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read gridPhase, centeredDerivativeWavenumber, ratio. Use the output convention below.
Compare a centered spatial derivative's mode factor with exact wavenumber. Require spacing > 0; gridPhase = k*h, centeredDerivativeWavenumber = sin(k*h)/h, ratio = sin(k*h)/(k*h), or one at k=0.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| wavenumber | Wavenumber | Required. Finite number. |
| spacing | Spacing | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| gridPhase | Grid Phase | Required. Finite number. |
| centeredDerivativeWavenumber | Centered Derivative Wavenumber | Required. Finite number. |
| ratio | Modified/exact derivative wavenumber; one at zero wavenumber by the limiting convention. | Required. Finite number. |
{
"input": {
"wavenumber": 0,
"spacing": 0.1
},
"output": {
"gridPhase": 0,
"centeredDerivativeWavenumber": 0,
"ratio": 1
}
}Limitations and assumptions
- Angular wavenumber and spacing must be reciprocal units; this is a local modified-wavenumber term, not full numerical dispersion 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
Use the complete mesh, transform convention and boundary conditions for a consistent numerical simulation or physical interpretation.
References
Similar or alternative tools
- Yee Grid Staggered Coordinate Offset
Return one staggered-grid coordinate.
- Poisson Stencil One Source Term
Scale one Poisson-stencil source contribution.