The governing equations, given above in Equation 6-7, are defined in the general scattered field formulation. Assuming that all the acoustic fields are the sum of a background (prescribed) field and the resulting scattered field, the total fields can be written as

where subscript t stands for total, subscript s for scattered, and subscript b for background. The scattered field is the field solved for (that is, the dependent variables p, u, and T). If no background acoustic field is defined (the default), the scattered field is equal to the total field. The governing equations and all boundary conditions are expressed in terms of the total fields. The equations solved for are thus, in general, for the frequency domain case given by

The background acoustic fields are defined by adding the Background Acoustic Fields feature. The feature has a user-defined option where all fields can be entered, either as analytical expressions or defined in terms of a solution to another study or model. The background acoustic fields feature also has a plane-wave option (in the frequency domain interface) that defines a plane propagating attenuated wave.

The plane wave option in the Background Acoustic Fields feature (in the frequency domain only) defines the following fields

where kb is the is the wave number of a plane propagating wave (in the direction nk) with viscous and thermal attenuation; see Ref. 3. The expressions given in Equation 6-14 are an exact solution to the governing equations Equation 6-13.