A set of linearised divergence equations (LDE) is proposed for acoustic propagation computations. The aim is to use LDE to overcome deficiencies in linearised Euler equations (LEE). The LDE uses curl-free velocity components in the equation. To solve the resulting Poisson equation efficiently, a one-dimensional Thomas scheme is implemented. Two validation exercises are undertaken against benchmark test cases. In validations it is stable with the presence of a sheared background mean flow, as against the conditionally stable LEE in time domain. The LDE also work for broadband acoustic propagation under the condition of high temperature ratios, e.g. exhaust out of an aeroengine core nozzle
The widely used linearised Euler equations (LEE) represent a class of acoustic approximation equations for sound propagation. They have their advantages over methods based on solutions of wave equations. However, these linear equations, when used in time-domains, can suffer from stability issues if a background shear flow is present. Other forms of linearsed formulations, e.g. acoustic perturbation equations (APE) are derived from the Navier-Stokes equations using acoustic velocity components. Inevitable high computing costs incurred by solving a Poisson equation is an issue for time-domain CAA methods. The practical versions of APE are also constrained by restrictive physics assumptions such as uniform background flow density, and often require excessive user intervention thereby rendering them difficult to use.
A set of governing equations are proposed for acoustic propagation computation. They overcome deficiencies in some of the existing governing equations for acoustic propagation and include broadband contents with improved efficiency.
Taking advantage of the stable character of the new formulation, the time step is increased and less high-order filtering is needed so overall computational cost is reduced.