As improving the performance of turbofan designs becomes increasingly difficult, manufacturers are looking to new technologies for the next generation of jet engines. An ``open rotor'' replaces the fan of the turbofan with a set of external rotors. This has the potential to offer a significant improvement in propulsive efficiency, but the design for low noise is a key challenge.

Hence, high fidelity noise prediction methods are needed to accurately predict and compare the noise of different designs. This thesis focuses on one set of methods based on the Ffowcs Williams-Hawkings (\fwh) equation. This equation is considered to be the most realistic description of aeroacoustic noise generation, as it is a direct rearrangement of the Navier-Stokes equations.

The \fwh\ equation is difficult to solve for realistic test cases such as an open rotor, and is susceptible to several types of error. This thesis categorises these errors as input'', neglection'' and ``discretisation'' errors. Discretisation errors arise from the need to integrate a discretised source field for the total noise, neglection errors result from needing to ignore part of the source field for practical reasons, and input errors relate to any errors caused by inaccurate input to the solver. The fundamental motivation of this thesis is to advance the understanding of neglection and discretisation errors and how they can be mitigated, in order to develop best practice solvers and methodologies for application to open rotors.

Dimensional analysis is combined with analytical flow solutions to develop a process for isolating and quantifying discretisation errors. This process is used to study a wide range of solver methodologies and select a best practice solver methodology for open rotor noise prediction. This first-of-a-kind study produces a solver methodology that reduces discretisation errors by an order of magnitude compared to an industry standard solver.

Previous research into neglection errors has shown that avoiding density perturbations in acoustic source terms can be beneficial. This thesis uses a generic aeroacoustic analogy to provide a new, physically intuitive method of incorporating a surface discontinuity that enables density perturbations to be avoided in a far more elegant manner than previous research.

The above method improvements are investigated using a modern open rotor rig test case. The results demonstrate that discretisation and neglection errors can be severe in realistic cases and the potential of the method improvements to significantly mitigate them.