Level Set Initialization Method

Level Set Initialization Method = {method_name} {parameter list}

Description / Usage

This card specifies the means by which the level set function is initialized. That is, it constructs from a representation of the starting interface shape, a value for the distance function at every node in the mesh. The syntax of the card is as follows:

{method_name}

A character string which identifies the initialization option desired. Choices for this string are: Projection, Exodus, Nodeset, Surfaces, SM_object.

{parameter list}

This is a variable parameter list specific to each option. The nature of it for each method is detailed in the syntax descriptions below.

Below are the exact syntax used for each initialization method, a brief description of the method and a specification of any additional required parameters.

Projection	This method computes the initial level set field by calling a user-specified routine which returns the signed distance function for a given point. It has no parameter list after its name.
Exodus	Using this card indicates that the initial level set field is to be read from the exodus file specified earlier (see FEM file and Initial Guess cards for read_exoII option). This card has no parameter list after its name.
Nodeset <integer1> EB <integer2>	This method establishes the initial location of the interface as the boundary between two element blocks. The value <integer1> is the nodeset identification number for an internal nodeset defined to exist at the interface between the two element blocks. The character string EB is required. The integer <integer2> is the element block id number to which positive values of level set function is going to be assigned.
Surfaces <integer>	This card establishes the initial level set function by referring to a set of primitive geometric objects. It is the easiest to use and the most general. The integer value <integer> is the number of surface objects that are used to construct the initial interface. This number of SURF object cards must follow this card. This is the syntax of the SURF object card: SURF = {object_name} {float list} {object_name}: a character string identifying the type of geometric object. Options are: PLANE, CIRCLE, SPHERE, SS, USER. {float list}: geometric parameters associated with each object as float values

The following is the syntax and description for each geometric object option, i.e., the “{object_name} {float list}” part of SURF

PLANE <nx. <ny> <nz> <d>	This card constructs a planar interface surface. The float values <nx>, <ny>, <nz> define a vector normal to this plane with the restriction that the sign of the vector must be such that it points from the negative side of the interface to the positive side of the interface. The float value <d> effectively represents the distance of the plane from the origin. Its value must be set, however, so that the dot product of any position vector to a point on the desired plane and the vector (nx,ny,nz) must be equal to <d> (it is a property of planes that this number is independent of the point on the plane that is chosen).
CIRCLE <cx> <cy> <radius>	This card constructs a circular interface surface in a two-dimensional domain. The float values <cx> <cy> identify the coordinates of the center of the circle. The float value <radius> establishes the radius of the curve. By definition, points interior to the circle are assigned negative level set function values.
SPHERE <cx> <cy> <cz> <radius>	This card constructs a spherical interface surface in a three-dimensional domain. The float values <cx> <cy> <cz> identify the coordinates of the center of the circle. The float value <radius> establishes the radius of the sphere. By definition, points interior to the sphere are assigned negative level set function values.
SS {ss_id}	This card uses an existing sideset in the problem as a defined geometric object for construction of an interface. The parameter <ss_id> identifies this sideset.
USER {user-defined float list}	This card indicates the user has defined an object function using the supplied parameter float list that returns a signed distance value when supplied with the coordinates of a point in space. This object function should appear in the function call user_init_object in the file user_pre.c.
SM_object {object_type} {object_name}	This card allows the user to initialize the level set location by using a piece of solid model geometry. The solid model object_type can be either FACE or BODY. A 2D initialization uses the boundary of the specified FACE (or surface) as the 0 level set. A 3D initialization uses the boundary of the specified BODY (or volume) as the 0 level set.

Examples

Two examples of initialization methods are provide below:

Level Set Initialization Method = Nodeset 20 EB 1

Level Set Initialization Method = Surfaces 3
    SURF = PLANE -1. 0. 0. -3.
        SURF = CIRCLE -2 0 1
        SURF = CIRCLE -3 0 0.5

Level Set Initialization Method = SM_object BODY my_blob

Technical Discussion

The Projection initialization method was developed early in the level set development process. It has since been superseded by other more easily used methods. It is still supported primarily for the use of developers. Users wanting a complicated interface shape for which they can supply an appropriate distance function should user the USER surface object option under the Surfaces initialization method.

The Exodus method deserves little comment. It should be used when restarting level set computations from a preexisting solution.

The Nodeset method allows the user to make use of the sophisticated solid body manipulation software in meshing packages like CUBIT. The procedure for using this method is to create a domain which contains two element blocks. The desired starting point for the interface should lie on the curve or surface which these two blocks have in common. A single nodeset should be defined over this entire curve or surface. The nodeset identification number should be the first integer parameter specified on the card. Also note that one of the blocks must be designated as the “positive” block. This means then when initialized the values of the level set function in this block will be positive. The values in the other block will be negative. Note that this initialization method can only by used for problems that have exactly two blocks, no more.

The Surfaces initialization method is the most useful method for initialization. It draws from the fact that it is relatively easy to determine the distance to simple geometric objects (planes, circles, spheres, etc.). Further, it permits initialization using more than one of these objects so that relatively complicated initial interface locations can be constructed. However, the user should recognize that this method is still somewhat unsophisticated in its approach so there are some caveats associated with its use. The primary point is that surface objects should never intersect anywhere within the domain of interest, otherwise it is more than likely that the starting interface shape will not be what the user expects.

The SM_object initialization method allows the user to use solid model geometry to initialize 2D and 3D level sets. Certain 2D geometries can be created using only Goma input commands (see FACE). Other 2D geometries, and all 3D geometries, can be accessed via an ACIS .sat file. The usual way to do this is for the user to create their desired geometry within Cubit (or, import solid model geometry from elsewhere into Cubit). Faces (or surfaces) should be created for 2D initialization, and bodies (or volumes) should be created for 3D initialization. The boundary of the object is used to initialize the level set. The geometry should be named within Cubit and exported to an ACIS .sat file via Cubit’s export acis “filename” ascii command. This same file should be read in via the ACIS file command in the Geometry Specifications section. The solid model geometry is then available for the Level Set Initialization Method command. (Note that the Geometry Specifications section usually comes after the Level Set Initialization Method command; this is OK).

References

GT-020.1: Tutorial on Level Set Interface Tracking in GOMA, February 27, 2001, T.A. Baer