Accumulator Theory: Boundaries

The Accumulator (Boundary) feature transfers information from rays to the boundaries they hit or pass through. Each defines a variable, called the accumulated variable, on the selected boundaries. The accumulated variable is discretized using constant shape functions, so its value if uniform over every mesh element and may be discontinuous between adjacent mesh elements.

The name of the accumulated variable is specified in the edit field in the section of the settings window. The default variable name, rpb, will be used in the remainder of this section when referring to the accumulated variable.

The options in the list are and . If is selected, the source term is divided by the surface area or length of the boundary mesh element when calculating each ray’s contribution to the accumulated variable. If is selected, no division by the surface area or length of the boundary element occurs.

The equations in the following section are valid for the type. The corresponding value of the accumulated variable for the type is

where V is the boundary element surface area (in 3D) or length (in 2D).

When is selected from the list, the accumulated variable in a boundary element gets incremented by the source term R whenever a ray freezes or sticks to the boundary:

where division by the mesh element area or length occurs because the accumulator is assumed to be of type . Thus the source term evaluated for an incident ray is uniformly distributed over the boundary element it freezes or sticks to.

If instead is selected from the list, then the accumulated variable gets incremented regardless of what type of ray-wall interaction occurs. Thus, it is possible for the same ray to increment the accumulated variable in many different boundary elements, or even in the same element multiple times.

Built-in Global Variables

By default, the boundary defines the following global variables:

Table 8-4: Built-in Global Variables for Boundary Accumulators
Name	Expression
<scope>.<name>_ave	Average of accumulated variable
<scope>.<name>_int	Integral of accumulated variable
<scope>.<name>_max	Maximum of accumulated variable
<scope>.<name>_min	Minimum of accumulated variable
<scope>.<name>_sum	Sum of accumulated variable over elements

Here, <scope> includes the physics interface name and the names the Accumulator and parent feature. For example, the average of the accumulated variable over a boundary may be called rac.wall1.bacc1.rpb_ave, where rac is the name of the Ray Acoustics interface, wall1 is the name of the parent Wall node, bacc1 is the name of the Accumulator node, and rpb is the accumulated variable name. These variables are all available in the menus during results evaluation.

These global variables are computed by defining a set of nonlocal couplings on the selection of the parent physics feature, such as the Wall feature to which the Accumulators are added. The following expressions for the global variables are used.

Table 8-5: Built-in Global Variable Definitions for Boundary Accumulators
Name	Expression
<scope>.<name>_ave	<wscope>.aveop(<scope>.<name>)
<scope>.<name>_int	<wscope>.intop(<scope>.<name>)
<scope>.<name>_max	<wscope>.maxop(<scope>.<name>)
<scope>.<name>_min	<wscope>.minop(<scope>.<name>)
<scope>.<name>_sum	<wscope>.intop(<scope>.<name>/<scope>.meshVol)

Here, <wscope> is the scope of the parent boundary feature, e.g. goprac.wall1.