Aerodynamic and aeroacoustic analysis of a pulsating internal flow by a multidomain weak collocation spectral method

A numerical methodology is presented for the coupled aerodynamic and aeroacoustic analysis of time dependent laminar viscous flows in general two-dimensional geometries. The overall procedure is constituted firstly by the solution of the incompressible Navier-Stokes equations and secondly by the solution of a linear evolution equation of second order in space and time which originates from Lighthill's acoustic analogy. A semi-implicit projection method is utilized for the time integration of the incompressible Navier-Stokes system, while a choice between a second order implicit Newmark scheme and a fourth order explicit Runge-Kutta-Nyström method is offered for the temporal discretization of the wave equation. The multidomain weak Legendre collocation spectral method on quadrilateral subdomain topologies is employed for the spatial approximation of both the fluid dynamic and the acoustic problems. A specific pulsating internal flow inside a plane constricted channel is selected as a representative application for the assessment of the capabilities of the proposed discrete algorithm. Numerous results are presented and discussed, so as to thoroughly demonstrate the behavior of the numerical procedure.