Comparative study of different non-reflecting boundary conditions for compressible flows

Abstract

The numerical simulation of hydrodynamic stability and aeroacoustic problems requires the use of high-order, low-dispersion and low-dissipation numerical methods. It also requires appropriate boundary conditions to avoid reflections of outgoing waves at the boundaries of the computational domain. There are many different methods to avoid wave reflection at the boundaries such as the buffer zone and boundary conditions based on characteristic equations. This paper considers the use of a methodology called perfectly matched layer (PML). The PML is evaluated for the simulation of an acoustic pulse in a uniform flow and the Kelvin–Helmholtz instability in a mixing layer using the linear and nonlinear form of the Euler equation. PML results are compared with other non-reflecting boundary condition methods in terms of effectiveness and computational cost. The other non-reflecting boundary conditions implemented were the buffer zone (BZ), widely used in aeroacoustic and hydrodynamic problems, and the energy transfer and annihilation (ETA), a very simple boundary condition to be implemented. The results show that the PML is an effective boundary condition method, but can be computationally expensive. The PML is also more complex to implement and requires careful stability analysis. The other boundary conditions, the BZ and the ETA, are also effective and may perform better than the PML depending on the flow conditions. These two methods have an advantage in terms of robustness and are much simpler to implement than the PML.