Three-dimensional non-reflective boundary conditions for acoustic simulations: far field formulation and validation test cases

In aeroacoustic simulations, non-reflective boundary conditions are necessary to minimize the acoustic waves reflected when disturbances leave the computational domain. In the present paper, far field boundary conditions are developed for a 3-D geometry. Two validation test cases involving respectively an acoustic pulse and an axisymmetric ring vortex in a uniform mean flow are also proposed. The solutions from linearized Euler equations show that the far field boundary conditions allow the exit of acoustic waves without generating significant spurious waves. The exit of vortical disturbances is more difficult to treat with efficiency because of their high magnitude. For this case, the implementation of a sponge zone is presented to decrease the amplitude of acoustic reflections.