Use the Asymptotic Far-Field Radiation node to prescribe open nonreflecting radiation conditions. The boundary condition is based on the asymptotic behavior of the acoustic waves in the far field. The condition is also known as the condition of Tam and Dong (see Ref. 17). The condition applies at boundaries far from a compact acoustic source. The waves must be assumed spherical in 3D (and 2D axisymmetric) or cylindrical in 2D. This means that the condition is valid in the limit where

where r is the distance from the source located at r0 and k is the wave number. The condition is formulated for the scattered field only, in problems involving an Background Acoustic Fields feature. The condition of Tam and Dong reads:

where η = 1 in the 3D (and 2D axisymmetric) spherical case and η = 2 in the 2D cylindrical case. In the frequency domain the time derivative is replaced by a multiplication with iω.

The acoustic perturbations behave differently than the entropy and vorticity waves. The acoustic waves propagate in all directions at the speed of sound (corrected by the background flow) while the entropy and vorticity waves are only convected by the background flow. The linearized Euler equations support both these waves so both have to be taken care off. At boundaries where the background flow leaves the computational domain, add the Outflow Boundary subfeature. A default Outflow Boundary node is added with a cleared selections.

When using the Asymptotic Far-Field Radiation condition careful meshing near the boundary needs to be considered as gradients of the degrees of freedom enter the equation. Because of this challenge, using the absorbing layers (ALs) in the time domain or the perfectly matched layers (PMLs) in the frequency domain is often more adequate and results in more accurate solutions.

Enter a Source location r0 (SI unit: m).