Extension of non-reflective outlet boundary condition for vortical disturbances

Imposing subsonic outlet boundary conditions for compressible ow simulations is still a challenging problem, since spurious re ections are occurring if unsteady disturbances leaving the domain. Most of the non-re ecting boundary conditions can be found in the literature performing very well if only acoustic perturbations are considered, but they are less e ective if there are vortical structures passing through the boundaries. This issue is true for both inlets and outlets, but in the current paper just outlets are considered in 2D and 3D. In the literature these spurious waves due to unsteady perturbation passing though the boundaries are called re ections. However, if a vortical structure is leaving the domain, the acoustic waves propagating back to the solution domain are rather created. In this sense, the original characteristic equations are modi ed such that the source terms responsible for these spurious waves could be identi ed and deactivated. In such a way, the vortical disturbances can pass the boundaries and therefore no more bu er zone is needed. In this paper, we used this approach to design non-re ecting outlet using residual distribution schemes to solve the bulk ow. We have developed the new boundary condition for both Linearized Euler Equations and Navier-Stokes Equations.