Amplitudes of characteristic waves and non-reflecting outflow conditions for high-fidelity numerical simulations

Non-reflecting boundary conditions are crucial for aeroacoustic simulations to prevent non-physical reflections at boundaries from contaminating the interior acoustic solutions. Various non-reflecting outflow conditions, mainly based on the characteristic theory, have been developed. By using a locally one-dimensional inviscid approximation, the characteristic wave amplitudes are identified as the projection of flow solutions into the eigenspace of the flux Jacobian matrix. When the weighted transverse terms are included, the definitions are essentially changed and produce different levels of non-physical reflections. This study aims to resolve the ambiguity in defining the amplitudes of characteristic waves. A new analysis in the frequency and wave number domain is proposed to identify the characteristic wave amplitudes in multidimensional space, and a second order in terms of the lateral wave number non-reflecting outflow condition that is more physically reasonable is derived. Numerical experiments are carried out to evaluate the performances of these non-reflecting conditions.