Noise barriers are a commonplace and effective method of noise control, and are used in a variety of industrial and civic situations. They are simply special barriers designed to absorb and reflect sound waves. However, their performance is reduced from theoretical estimates when placed in front of a reflective noise source, or when two barriers are placed in a parallel around the noise source, with reductions on the predicted insertion loss (IL) on the order of 10 dB. This is due to multiple reflections and over-the-top scattering. To combat this problem, we have designed a new Wave Trapping Barrier (WTB) to control the direction of reflected noise and reduce overhead scattering. This has been shown in previous work to be an effective means of reducing noise. In this work, we use a modified Chebyshev expansion of the acoustic wave propagator to computationally model and simulate a wave trapping barrier in action, and investigate an optimum tilting angle for the WTB. We found that varying this angle gave a range of overall IL gains of 2-3 dB, with a peak gain in IL due to overhead scattering at an angle of ∼56°, with a gain of up to 2.8 dB, for a 2m by 2m enclosure, showing that controlling the tilting gives a not-insignificant gain in IL.