Time-domain implementation of nonreflecting boundary-conditions for the nonlinear Euler equations

The present paper studies nonreflecting boundary-conditions for the 2-D unsteady nonlinear Euler equations, applied to the propagation of monochromatic pressure-waves in a uniform mean flow. Various boundary-conditions (1-D nonlinear, approximate linearized 2-D, and exact linearized 2-D) are compared for a wide range of both propagating and decaying waves. An original methodology, based on a moving-averages technique, is developed for the application of the exact linearized boundary-conditions, which requires the computation of 2-D (space–time) Fourier coefficients. It is shown that the exact linearized boundary-conditions yield very low reflection, and also that the approximate conditions may perform poorly in difficult cases. The reflection-coefficient shows some correlation with the group-velocity (direction and Mach-number) of the reflected waves, suggesting that proposed nonreflecting boundary-conditions should always be validated against the entire range of group-velocities.