Stable time-domain CAA simulations with linearised governing equations

In time-domain simulations of sound propagation, solutions obtained from linearised Euler equations may suffer from numerical Kelvin-Helmholtz instabilities in the presence of a sheared mean flow. The Kelvin-Helmholtz instabilities are vortical disturbances that can grow boundlessly and eventually contaminate the solution field. Several methods were developed to eliminate this numerical vulnerability. However, each method relies on different key assumptions that can affect the accuracy of the solution. In this work, new methods are proposed to facilitate a stable and accurate numerical result. An artificial damping term is proposed with adaptive adjustment to stabilise the simulation by introducing additional damping effects on vortical components. Three gradient term modification methods are developed to allow accurate acoustic field computation with a minor side effect. The proposed methods are tested on four benchmark cases: i) acoustic wave refraction through a strongly sheared mean flow, ii) acoustic wave refraction through a weakly sheared mean flow, iii) vortical wave propagation, and iv) acoustic mode radiation from an unflanged duct. It is demonstrated that the proposed methods can suppress the numerical stability and obtain an accurately solved acoustic field.