aeroacoustics volume 13 · number 3 & 4 · 2014 – pages 261 – 274 261 A comparative study of accuracy of shock capturing schemes for simulation of shock/acoustic wave interactions Dmitry V. Khotyanovsky 1,2 , Alexey N. Kudryavtsev 1,2 and Andrey Yu. Ovsyannikov 3 1 Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of Sciences, 4/1, Institutskaya st., Novosibirsk, 630090, Russia khotyanovsky@itam.nsc.ru, alex@itam.nsc.ru 2 Novosibirsk State University, 2, Pirogova st., Novosibirsk, 630090, Russia 3 Center for Turbulence Research, 488 Escondido Mall Building 500, Stanford University, Stanford, CA 94305-3024, USA aovsyann@stanford.edu Received May 1, 2013; Revised April 21, 2014; Accepted May 1, 2014 ABSTRACT We simulate transmission of a small-amplitude disturbance wave through a shock wave. Results of our numerical experiments performed with different high-order shock-capturing schemes show that the capability of a scheme to correctly predict the amplification of the disturbances crucially depends on the Riemann solver used in evaluation of numerical fluxes. Incorrectly high amplification rates are produced by the solvers resolving shock waves sharply, with no interior points in numerical profiles of steady shock waves. In particular, both the exact Riemann solver and the popular Roe flux difference splitting demonstrate such unphysical behavior. A possible explanation of such behavior is proposed. More dissipative solvers, such as the global Lax–Friedrichs splitting, produce transmission coefficients close to the predictions of linear theory. 1. INTRODUCTION Interaction of small disturbances, such as acoustic waves, with a shock wave is relevant to many fundamental problems and applications of aeroacoustics in supersonic flows. For example, shock wave interactions with near-wall boundary layers and free shear flows result in a significant increase in intensity of turbulent fluctuations 1,2 . When the flow disturbance amplitude is small, linear interaction analysis (LIA) can be used to predict the amplification rate. In the elementary case of normal incidence of sound on the shock wave, this was done independently by Blokhintsev 3 and Burgers 4 for the problem of a sound receiver in a supersonic flow. The general case of the inclined incidence of an acoustic wave on a shock wave was considered later in a series of papers. The complete solution of the problem was obtained by Dyakov 5,6 , who