A non-local computational boundary condition for duct acoustics

A nonlocal boundary condition is formulated for acoustic waves in ducts without flow. The ducts are two-dimensional with constant area, but with variable impedance wall lining. Extension of the formulation to three-dimensional and variable area ducts is straightforward in principle, but requires significantly more computation. The boundary condition simulates a nonreflecting wave field in an infinite duct. It is implemented by a constant matrix operator which is applied at the boundary of the computational domain. An efficient computational solution scheme is developed which allows calculations for high frequencies and long duct lengths. This computational solution utilizes the boundary condition to limit the computational space while preserving the radiation boundary condition. The boundary condition is tested for several sources. It is demonstrated that the boundary condition can be applied close to the sound sources, rendering the computational domain small. Computational solutions with the new nonlocal boundary condition are shown to be consistent with the known solutions for nonreflecting wave fields in an infinite uniform duct.