How the three-dimensional geometry of computational domain(s) affects the accuracy of non-reflective boundary conditions in acoustic simulation

Describing and simulating acoustic wave propagation can be difficult and time consuming; especially when modeling three-dimensional (3D) problems. As the propagating waves exit the computational domain, the amplitude needs to be sufficiently small otherwise reflections can occur from the boundary influencing the numerical solution. This paper will attempt to quantify what is meant by `sufficiently small' and investigate whether the geometry of the computational boundary can be manipulated to reduce reflections at the outer walls. The 3D compressible Euler equations were solved using the discontinuous Galerkin method on a graphical processing unit. A pressure pulse with an amplitude equivalent to 10% of atmospheric pressure was simulated through a modified trumpet within seven different geometries. The numerical results indicate that if the amplitude of the pulse is less than 0.5% of atmospheric pressure, reflections are minimal and do not significantly influence the solution in the domain. Furthermore, the computational region behind the bell can be neglected greatly reducing the required memory and run time.