Stable Finite Element Formulation for the Perturbed Convective Wave Equation

In computational aeroacoustics for low Mach numbers, the acoustic perturbation equations (APE) allow for a precise separation between the physical flow quantities and the acoustic quantities. By introducing the acoustic
scalar potential, this set of partial differential equations can be rewritten without any approximations by the Perturbed Convective Wave Equation (PCWE). This second order partial differential equation in space and time fits well to be solved by the Finite Element (FE) method. However, one has to take care that the convective operator, which is non-symmetric, is formulated in such a way that the discrete system preserves non-symmetry. Otherwise, spurious modes occur, which will strongly disturb the numerical solution and the computation may
even become unstable.