Description
Calculate nominal cell-center and node coordinates from a supplied uniform grid.
Numerical physics calculations depend on discretization, index conventions, boundary conditions and model units. A local force kick is only part of an integration method, a stencil residual is not a solved field, and a one-sided power weight is not a spectral-density normalization. Floating-point resolution also limits grid and coordinate representations.
Calculate nominal cell-center and node coordinates from a supplied uniform grid.
When to use this tool
Use Grid Node Cell Center Offset when you already have origin, cellWidth, zeroBasedCellIndex and need to calculate nominal cell-center and node coordinates from a supplied uniform grid.
How to use the tool and how it works
- Enter origin, cellWidth, zeroBasedCellIndex. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read cellCenter, leftNode, rightNode. Use the output convention below.
Require cellWidth>0 and zeroBasedCellIndex a nonnegative safe integer; center=origin+(index+0.5)*width, nodes=origin+index*width and origin+(index+1)*width.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| origin | Origin | Required. Finite number. |
| cellWidth | Cell Width | Required. Finite number; strictly above 0. |
| zeroBasedCellIndex | Nonnegative safe whole index; a half-cell offset can still be lost near the precision limit. | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| cellCenter | Cell Center | Required. Finite number. |
| leftNode | Left Node | Required. Finite number. |
| rightNode | Right Node | Required. Finite number. |
{
"input": {
"origin": 0,
"cellWidth": 2,
"zeroBasedCellIndex": 3
},
"output": {
"cellCenter": 7,
"leftNode": 6,
"rightNode": 8
}
}Limitations and assumptions
- Large indices can lose half-cell resolution in floating point. No grid bounds, mesh, physical coordinates or discretization quality is verified.
- 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 discretized model, integration algorithm and boundary treatment. Assess convergence, conservation and stability with the full calculation; individual residuals, CFL components, relaxation terms and index mappings do not establish numerical accuracy or physical validity.
References
Similar or alternative tools
- Periodic Ghost Cell Index
Map a supplied storage slot to a periodic interior source index.
- Quadrature Node Affine Map
Affinely map supplied reference quadrature nodes and weights to an interval.