Low Machnumber aeroacoustics – A direct one-grid approach

Aeroacoustic simulations for low Machnumbers on the basis of the compressible Navier–Stokes equations result into a stiff multiscale problems, where the acoustic wave length and the wave length of the corresponding velocity perturbations are located on different scales and the speed of sound is larger by orders than the flow convection speed. Usually, aeroacoustic methods separates the multiple scales by solving the fluid flow without any acoustics, while the acoustic field is simulated afterwards or the stiffness is reduced by preconditioning techniques. An alternative approach, for which we restrict ourselves to smooth solutions, is presented here that solves the acoustic and the flow field fully coupled on an unstructured grid, which is designed taking into account the different length scales. However, the use of such an highly unstructured grid together with the stiffness of the problem, gives rise to a new numerical challenge: finding the optimal time step size for an equally distributed numerical error on the whole domain. The problem is solved using a fully implicit time discretization method. Due to the expected multiscale solution, the linear algebraic system of equations is solved with a geometric multigrid solver. It is possible to set up a multigrid procedure with Machnumber independent convergence rates, hence the solver is robust against the Machnumber.