On Boundary Conditions for Compressible Flow Simulations

Global linear stability analysis of open flows in truncated domains suffers from imperfect boundary conditions, leading to either spurious wave reflections (in compressible cases) or to non-local feedback due to the elliptic nature of the pressure equation (in incompressible cases). A novel approach is introduced to solve such an issue. The technique is based on the analytical continuation of the spatial coordinate system in such a way that undesired waves, e.g. reflected acoustic waves, do not affect the spatial region of interest. Such a method is named Complex Mapping (CM) technique and it can be understood as a particular case of a more general family of non-reflecting boundary conditions, Perfectly Matching Layer (PML). Nonetheless, the straightforward application of the latter increases the number of degrees of freedom. A similar situation is observed with the application of sponge or buffer regions, which require a large damping region of the order of several wavelengths of the wave to damp, e.g. forward acoustic wave. We demonstrate the application of simple complex mappings in the hole-tone configuration, namely a jet passing through two successive circular holes. In this configuration the use of complex mapping is particularly efficient with respect to sponge techniques, because the low Mach numbers involved in the computations imply large sponge regions.