Gradient Term Filtering for Stable Sound Propagation with Linearized Euler Equations

A new, stable gradient term filtering (GTF) method is applied to time-domain linearised Euler equations (LEE) to compute sound propagation problems. The method employs a Laplace operator as a filter to obtain acoustic wave components. Through the filtering process, both the Kelvin-Helmholtz and the Rayleigh–Taylor instabilities can be removed from the solution process. Stability analysis confirms the stable behaviour of the solution in the presence of a sheared background mean flow, as against the conditional stability of LEE and gradient term suppression (GTS) methods. In accounting for vortical wave propagation, a curl operator can be conventionally utilised to obtain two-dimensional vortical wave components. Several benchmark test cases are studied to validate the proposed methods. Tests show that the proposed method can obtain stable solutions for acoustic wave propagation and is capable of modeling vortical interactions.