# 9.10. Variable Interpolation

The variable interpolation command block is used to transfer data from one block or surface to another. Generally the transferred data is output data that will be used for a subsequent analysis. As an example the variable interpolation command block was created primarily to aid acoustic analysis where the derivative of void element volume is mapped from the structural Sierra/SM mesh to a background acoustic mesh for use in Salinas.

    BEGIN VARIABLE INTERPOLATION [<string>var_interp_name]
      TRANSFER TYPE = INTERPOLATE FROM NEAREST FACE|
        SUM TO NEAREST ELEMENT
      SOURCE VARIABLE = ELEMENT|NODAL|
        SURFACE NORMAL NODAL <string>source_var_name
      SOURCE ELEMENT BLOCK = <string>source_block
      SOURCE ASSEMBLY BLOCK = <string>source_assembly
      SOURCE SURFACE = <string>source_surface
      SOURCE ASSEMBLY SURFACE = <string>source_assembly
      TARGET VARIABLE = ELEMENT|FACE|NODAL
        <string>target_var_name
      TARGET DERIVATIVE VARIABLE = ELEMENT|FACE|NODAL
        <string>target_deriv_var_name
      TARGET SURFACE = <string>target_surface
      TARGET ASSEMBLY SURFACE = <string>target_assembly
      SEARCH TOLERANCE = <real>search_tol
      PROXIMITY SEARCH TYPE = RAY SEARCH|SPHERE SEARCH
      RAY SEARCH DIRECTION = <real>vecx <real>vecy <real>vecz
      ONE WAY RAY SEARCH DIRECTION = <real>vecx <real>vecy <real>vecz
      RAY SEARCH DIRECTION = ORTHOGONAL TO LINE <real>p1x
        <real>p1y <real>p1z <real>p2x <real>p2y <real>p2z
      RAY SEARCH DIRECTION = TARGET SURFACE NORMAL

      ACTIVE PERIODS = <string list>period_names
      INACTIVE PERIODS = <string list>period_names
    END [VARIABLE INTERPOLATION <string>var_interp_name]

The command `TRANSFER TYPE` can be set to either `INTERPOLATE FROM NEAREST FACE` or `SUM TO NEAREST ELEMENT`. The `TRANSFER TYPE` restricts the commands that can be used in conjunction with it.

When `TRANSFER TYPE` is set to `INTERPOLATE FROM NEAREST FACE` the available commands are restricted to:

    BEGIN VARIABLE INTERPOLATION [<string>var_interp_name]
      TRANSFER TYPE = INTERPOLATE FROM NEAREST FACE
      SOURCE VARIABLE = NODAL|SURFACE NORMAL NODAL
        <string>source_var_name
      SOURCE SURFACE = <string>source_surface
      SOURCE ASSEMBLY SURFACE = <string>source_assembly
      TARGET VARIABLE = NODAL <string>target_var_name
      TARGET DERIVATIVE VARIABLE = NODAL <string>target_deriv_var_name
      TARGET SURFACE = <string>target_surface
      TARGET ASSEMBLY SURFACE = <string>target_assembly
      SEARCH TOLERANCE = <real>search_tol
      PROXIMITY SEARCH TYPE = RAY SEARCH|SPHERE SEARCH
      RAY SEARCH DIRECTION = <real>vecx <real>vecy <real>vecz
      ONE WAY RAY SEARCH DIRECTION = <real>vecx <real>vecy <real>vecz
      RAY SEARCH DIRECTION = ORTHOGONAL TO LINE <real>p1x
        <real>p1y <real>p1z <real>p2x <real>p2y <real>p2z
      RAY SEARCH DIRECTION = TARGET SURFACE NORMAL
    END [VARIABLE INTERPOLATION <string>var_interp_name]

For `TRANSFER TYPE` = `INTERPOLATE FROM NEAREST FACE`, a given point on the target surface is mapped to the closest point on the source surface. At that closet source point the source variable is interpolated. The interpolated value is then copied from the interpolated source point to the target point. Optionally if the `SURFACE NORMAL NODAL` command is being used and the variable being transferred is a vector then only the surface normal component of that variable will be transferred. This is useful for several applications involving transferring solid mesh quantities such as velocity to a reference mesh modeling a fluid (e.g., air). In such applications only the surface normal vibration is relevant to the air acoustic solve.

When `TRANSFER TYPE` is set to `SUM TO NEAREST ELEMENT` the available commands are restricted to:

    BEGIN VARIABLE INTERPOLATION [<string>var_interp_name]
      TRANSFER TYPE = SUM TO NEAREST ELEMENT
      SOURCE VARIABLE = ELEMENT <string>source_var_name
      SOURCE ELEMENT BLOCK = <string>source_block
      SOURCE ASSEMBLY BLOCK = <string>source_assembly
      TARGET VARIABLE = ELEMENT <string>target_var_name
      TARGET DERIVATIVE VARIABLE = ELEMENT
        <string>target_deriv_var_name
      TARGET SURFACE = <string>target_surface
      TARGET ASSEMBLY SURFACE = <string>target_assembly
      SEARCH TOLERANCE = <real>search_tol
      PROXIMITY SEARCH TYPE = RAY SEARCH|SPHERE SEARCH
      RAY SEARCH DIRECTION = <real>vecx <real>vecy <real>vecz
      ONE WAY RAY SEARCH DIRECTION = <real>vecx <real>vecy <real>vecz
      RAY SEARCH DIRECTION = ORTHOGONAL TO LINE <real>p1x
        <real>p1y <real>p1z <real>p2x <real>p2y <real>p2z
    END [VARIABLE INTERPOLATION <string>var_interp_name]

For `TRANSFER TYPE` = `SUM TO NEAREST ELEMENT`, a given element in the source block computes its centroid. Then the closest face to that centroid on the target surface is found. The source element value is summed to the element attached to that target face.

The command `SOURCE VARIABLE` specifies the variable type, `ELEMENT`, `GLOBAL`, or `NODAL`, and the name of the source variable `source_var_name`.

The command `SOURCE ASSEMBLY BLOCK` specifies the name of the source assembly of blocks `source_assembly`.

The command `SOURCE SURFACE` specifies the name of the source side set `source_surface`.

The command `SOURCE ASSEMBLY SURFACE` specifies the name of the source assembly of side sets `source_assembly`.

The command `TARGET VARIABLE` specifies the variable type, `ELEMENT`, `FACE`, or `NODAL`, and the name of the target variable `target_var_name`. The target variable must exist. If necessary, a target variable can be created using the `BEGIN USER VARIABLE` command block (Section 10.2.4).

The command `TARGET DERIVATIVE VARIABLE` can be used to optionally compute the time derivative of the target variable. This command specifies the type of variable, `ELEMENT`, `FACE`, or `NODAL`, and the name of the variable to store the derivative, `target_deriv_var_name`. The target derivative variable must exist. If necessary, a target variable can be created using the `BEGIN USER VARIABLE` command block (Section 10.2.4).

The command `TARGET SURFACE` specifies the name of the target side set `target_surface`.

The command `TARGET ASSEMBLY SURFACE` specifies the name of the target assembly of side sets `target_assembly`.

The command `SEARCH TOLERANCE` specifies a search distance for use in the proximity search.

The command `PROXIMITY SEARCH TYPE` can be set to either `RAY SEARCH` or `SPHERE SEARCH`. When `PROXIMITY SEARCH TYPE = SPHERE SEARCH` the `SEARCH TOLERANCE` is used as the radius for closest point searches. When `PROXIMITY SEARCH TYPE = RAY SEARCH` the `SEARCH TOLERANCE` and any `RAY SEARCH DIRECTION` are used together to form rays with lengths equal to the `SEARCH TOLERANCE`. If the `RAY SEARCH DIRECTION` command is used then the rays will extend in both the positive and negative directions. If the `ONE WAY RAY SEARCH DIRECTION` is used the rays will extend in only the positive direction. The one way rays are currently only available with the explicitly defined search direction vector. Faces penetrated by a ray are included in the set of faces for determining the closest point.

The commands `RAY SEARCH DIRECTION` and `ONE WAY RAY SEARCH DIRECTION` specify a search direction for the `PROXIMITY SEARCH = RAY SEARCH DIRECTION` case. A `RAY SEARCH DIRECTION` or `ONE WAY RAY SEARCH DIRECTION` can be specified directly with three values, `vecx`, `vecy`, and `vecz`. Alternatively, `RAY SEARCH DIRECTION` can be calculated through options `ORTHOGONAL TO LINE` or `TARGET SURFACE NORMAL`. For `ORTHOGONAL TO LINE` the search direction is the vector between a given point and the closest point on the infinite line specified with the two points `p1x, p1y, p1z` and `p2x, p2y, p2z`. For `TARGET SURFACE NORMAL` the search direction is the nodal normal vector calculated from the `TARGET SURFACE`.

## 9.10.1. Variable Interpolation Examples

The variable interpolation commands are complicated and best explained by the following example of a likely use case for this capability.

Example 1: Transferring volume infusion term to acoustic analysis. The example geometry is shown in Fig. 9.16(a) run with the below syntax.

    BEGIN VARIABLE INTERPOLATION
      TRANSFER TYPE = SUM TO NEAREST ELEMENT
      SOURCE VARIABLE = ELEMENT volume_first_derivative
      SOURCE ELEMENT BLOCK = block_1
      TARGET VARIABLE = ELEMENT volume_change_rate
      TARGET SURFACE = surface_2
      SEARCH TOLERANCE = 1.0e-3
    END [VARIABLE INTERPOLATION <string>var_interp_name]

The volume derivatives are computed void elements (red) in source block one. At the centroid of each of these elements the closest facet on the target surface `surface_2` is found (green). The volume derivatives are then summed to the elements attached to the target surface faces (following blue arrows). In this way the change of volume of structural void elements can be mapped to gas source term in a subsequent Salinas acoustic analysis. A similar boundary condition can be used to map structural energy source terms for a subsequent thermal analysis.

Example 2: Transferring surface motion for acoustic analysis. The example geometry is shown in Fig. 9.16(b) run with the below syntax.

    BEGIN VARIABLE INTERPOLATION [<string>var_interp_name]
      TRANSFER TYPE = INTERPOLATE FROM NEAREST FACE
      SOURCE VARIABLE = SURFACE NORMAL NODAL velocity
      SOURCE SURFACE = surface_1
      TARGET VARIABLE = NODAL surface_motion
      TARGET SURFACE = surface_2
      SEARCH TOLERANCE = 1.0e-3
      PROXIMITY SEARCH TYPE = RAY SEARCH|SPHERE SEARCH
    END [VARIABLE INTERPOLATION <string>var_interp_name]

The source surface velocities (solid red arrows) are first restricted to the surface normal (dotted red errors). These normal velocities define a velocity distribution on the source source (thin red line). The velocity distribution at each node of the target surface (green arrows) found by spatial interpolation of the source surface normal velocity. In this way the solid normal surface motion can be mapped as a boundary condition on a subsequent Salinas acoustic analysis at the exterior fluid domain. A similar boundary condition can be used to drive a variety of one way interface based fluid/structure or other code-to-code couplings.

Note that a general acoustic source mapping will include both a volume source term and a surface motion boundary condition defined in two variable interpolation blocks.

(a) Nearest element.
(b) Nearest face.

Fig. 9.16 Variable interpolation options.