Direct Numerical Aeroacoustics for low Mach numbers using one Unstructured Grid

Abstract

Using an unstructured grid, for which the mesh size is adapted to the local flow and acoustic solution, one can reduce the number of unknowns needed for a direct aeroacoustic simulation. The compressible Navier-Stokes equations for Mach numbers 0 <M <1 are considered. However, the unstructured grid together with the increasing stiffness of the problem for M → 0 reveals new numerical challenges. One is, to find an optimal time step size, that will reveal an equal numerical error distribution on the computational domain. Therefore, CFL-numbers greater than 1 are required, so that an implicit approach is chosen to overcome this complexity. The multigrid method used to solve the resulting algebraic system of equations is robust against the Mach number. Hence, the convergence rate does not deteriorate for M → 0. The accuracy of the time and space discretisation is investigated with respect to their numerical dispersion and diffusion properties. Furthermore, the order of the space discretisation is increased with a τ -extrapolation method, which is embedded into the multigrid procedure. The accuracy of the method and the reduction of unknowns is demonstrated by numerical simulations.