Compound waves in a higher order nonlinear model of thermoviscous fluids

A generalized traveling wave ansatz is used to investigate compound shock waves in a higher order nonlinear model of a thermoviscous fluid. The fluid velocity potential is written as a traveling wave plus a linear function of space and time. The latter offers the possibility of predicting the outcome of interacting shock waves, i.e. shock jump heights and wave velocities after collisions and overtakes. The stability of the linear solution part is investigated and a criterion for its stability is determined. For a number of instances, the numerical results show formation of rarefaction waves. By using a similarity transformation, analytical expressions for these rarefaction waves are found in the limit of no dissipation. Examples of compound shock waves are illustrated by numerical simulations.