## Description

The *Expansion Ratio (Fidelity)* examine metric is available when at least one block is selected for
*Examine*. This metric is compatible with the Fidelity *Expansion Ratio* metric.

The *Expansion Ratio* is a measure of the size variation between two adjacent volume cells *i* and *j*. Assuming that both adjacent
cells have a common face *f*, the *Expansion Ratio* between them is computed as follows:

`ER`_{i,j} = max [D_{i,f}/D_{j,f}, D_{j,f}/D_{i,f}]

where:

`ER`_{i,j}

= Expansion ratio between cell *i* and its adjacent cell *j*

- Cells
*i* and *j* are hexahedral:
`D`_{i,f}

= Distance between the centroid of the shared face *f* and the centroid of the opposite face of cell *i*

`D`_{j,f}

= Distance between the centroid of the shared face *f* and the centroid of the opposite face of cell *j*

- Cells
*i* and/or *j* are not hexahedral:
`D`_{i,f}

= Distance between the centroid of the shared face *f* and the centroid of the volume cell *i*

`D`_{j,f}

= Distance between the centroid of the shared face *f* and the centroid of the adjacent volume cell *j*

The final expansion ratio for cell *i* is computed by taking the maximum of all the expansion ratios computed for each adjacent
cell *j*:

`ER`_{i} = max_{j} [ER_{i,j}]

This function is calculated across entity boundaries when adjacent entities are also selected for *Examine*.

**Tip:** The *Expansion Ratio* function is an excellent diagnostic for finding cell size discontinuities at block interfaces.