Numerical Computation of the Radiation and Refraction of Sound Waves Through a Two-Dimensional Shear Layer

The linearized Euler equations are numerically solved to compute the radiation and refraction of sound waves through a two-dimensional shear layer. The dispersion-relation-preserving (DRP) scheme is employed for spatial discretization and the low dispersion and low dissipation Runge-Kutta (LDDRK) algorithm is used for time integration. The linearized Euler equations do not only provide a solution for sound propagation, but also admit unstable solutions and instability waves can thereby be triggered. These have to be suppressed numerically. The main objective of this research is to accurately capture the sound radiation and refraction through the shear layer while simultaneously suppressing the instability waves. To realize this aim, two methods are proposed in this paper. The first is to employ a multi-size mesh coupled with a spatial filter, while the second involves the introduction of a source filter into the linearized Euler equations. Numerical test results are presented to demonstrate the feasibility of the two proposed techniques.