Capturing matched layer at absorbing boundary with finite volume schemes

•The matched layer is automatically captured at absorbing boundary.•The absorbing boundary condition is hence extremely simple but robust.•It is embedded in finite volume schemes, not related to other nonreflecting conditions.•It is established via Fourier analysis and plane waves, theoretically, reflection = 0.•Non-trivial test examples in 1D–3D spaces are demonstrated.

In compressible flow computations, an important treatment for absorbing boundary condition (ABC) is to create a matched layer at the boundary, as in the well-known PML (perfectly matched layer) method. In the present paper, it is shown that with cell-centered finite volume (FV) schemes, the matched layer can be captured directly as a discontinuity across the absorbing boundary, rendering an extremely simple yet robust ABC. The new ABC is inherently embedded in FV schemes of cell-centered type, and often associated with the captured matched layer, which serves to match the flow variables across the boundary. It has been used empirically for years and was found to have no direct relation to any existing nonreflecting boundary condition (NRBC). Instead, it is attributed to the shock-capturing capability of the FV scheme, as well as a nonreflecting (NR) observation that for any scheme, no spurious reflection is generated at any interior point of the domain. A Fourier analysis with plane waves is employed to the local Euler solution to justify the NR observation and the ABC is consequently established.The ABC performs perfectly with zero reflection in one dimensional space. In multi-dimensional spaces, the phase error and reflection due to discretization are discussed. With appropriate grid resolution at the boundary, one can always suppress the spurious reflection to any designated level. Several non-trivial numerical examples in one and multi-dimensional spaces are tested to demonstrate its robustness.