Level Set Renormalization Tolerance#

```Level Set Renormalization Tolerance = <float>
```

Description / Usage#

This parameter provides a means for controlling how often renormalization (redistancing) operations are performed on the level set function as it evolves by fixing the size of the deviation allowed between the average absolute magnitude of the level set function gradient near the level set interface and unity, the theoretical value observed for a pure distance function.

<float>

Value of the tolerance, the allowable deviation.

The range of this parameter is any positive real number, however, it is rare to use values smaller than 0.1 or larger than 5.0. The value of the tolerance defaults to 0.5 if this card is not specified.

Examples#

This is a sample renormalization card:

```Level Set Renormalization Tolerance = 0.05
```

Technical Discussion#

One of the key properties of the level set function is that it is a smooth function near to the interface. In particular, if the level set function is a distance function then the magnitude of its gradient on the zero level contour should always be unity. This fact is used to provide a criterion for invoking a renormalization procedure. The gradient of the level set function is found within a fixed region around the zero level set contour (see Level Set Control Width). The integrated average of the magnitude of this vector is determined and compare to unity. Should this difference differ by greater than the value for Renormalization Tolerance identified on this card, a renormalization procedure will presently be initiated.

FAQs#

What is a proper value for this parameter? Values on the order of unity should work well. Renormalization based on gradient can be disabled completely by choosing a very large value for this parameter. Conversely, a very small value will always result in a renormalization step.

Is it possible to renormalize too often? Yes. Renormalization is an extraphysical procedure designed solely to improve the numerical performance of the interface tracker. As such, it can add or subtract volume to or from the phases represented by the interface contour. Renormalizing too often, therefore, can result in errors being introduced. The renormalization procedure, Huygens_Constrained, attempts to mitigate this effect.