# Level Set Length Scale#

Level Set Length Scale = <float>


## Description / Usage#

On this card, the user specifies a single char_string.

<float>

This value represents the size of the region around the zero level set function contour in which interfacial physical quantities, for example, surface tension, will be present.

Stability and conservation of phase volume are dependent upon this value to a significant degree. Experimentation has revealed that this float value should be between two and three times the average linear dimension of the elements in the mesh.

## Examples#

A typical length scale input card looks like:

Level Set Length Scale = 0.3


## Technical Discussion#

The level set method is an embedded interface method. That is, the location of the interface is not known explicitly as a geometric parameter of the problem, but rather it is abstracted as a level contour of a higher dimensional function. This is convenient in many ways, but it does mean that phenomena associated with the interface, for example, surface tension, must enter the problem spread over a region near the zero level set contour. The Level Set Length Scale sets the size of this region.

A good example of the application of the Level Set Length Scale parameter is in how surface tension is included in problems using level set interface tracking. The following tensor is added to the fluid momentum equation:

$\underline{\underline{T}} = \sigma \delta_{\alpha} \left( F \right) \left( \underline{\underline{I}} - \underline{n} \,\underline{n} \right)$

where $$F$$ is the level set function itself, $$\underline{n}$$ is the unit normal to the level set contour, $$\underline{\underline{I}}$$ is the unit tensor, $$\sigma$$ the surface tension, and $$\delta_{\alpha} \left( F \right)$$ is a “smooth” Dirac function given by:

$\delta_{\alpha} \left( F \right) = \lvert \nabla F \rvert \frac{1 + \cos \left( \pi F/\alpha \right)}{2 \alpha}, \quad \lvert F \rvert \leq \alpha$

In this example, the parameter $$\alpha$$ would be equal to one-half the Level Set Length Scale value specified on this card.

## FAQs#

How should the Length Scale value be chosen? Trial and error is often the best method to determine an appropriate value for this parameter. However, experience has shown that values for Level Set Length Scale that are between two and three times the average element linear dimension seem to work best.