Numerical analysis of the nonlinear propagation of plane periodic waves in a relaxing gas

The waves propagating from an oscillating plane piston into a vibrationally relaxing gas are calculated by an exact numerical method ignoring viscosity and heat conduction. Secondary effects due to the starting of the piston from rest and to acoustic streaming can be eliminated from the calculated flows, leaving a truly periodic progressive wave which can be analysed and compared with approximate solutions. It is found that for moderate amplitude waves nonlinearity is only important as a convective effect which produces higher harmonics, whereas dissipation is adequately described by linear theory.