Acoustic scattering in a rarefied gas: Solving the R13 equations in spherical polar coordinates

Abstract

In some circumstances, sound waves in a rarefied gas can be studied using a linearised form of the regularised 13‐moment equations of Struchtrup and Torrilhon. We build solutions of those equations in spherical polar coordinates using vector spherical harmonics. We first solve a reduced system of equations (with 11 unknowns) after introduction of a force vector (divergence of the stress). We then show that the stresses themselves can be recovered by solving five additional equations. The results obtained are expected to be useful for problems such as acoustic scattering of a plane wave by a sphere in a rarefied gas.