![]() ![]() This is illustrated by numerical results using a pseudospectral method. Analysis of the shock region then reveals the same richness of structure seen in the travelling wave case, with subtle changes in shock structure as the disturbance decays. We establish parameter ranges in which the waveform is described by an outer solution (obtained using characteristics) and a thin shock region. We then consider the propagation of a rectangular pulse. For a single relaxation mode, if the amplitude P is less than a certain critical value then the transition is controlled entirely by the relaxation mode whereas for larger P, a thin viscous sub-shock arises. We begin by considering travelling wave solutions for the propagation of a pressure step, of amplitude P, in the small viscosity limit. Each relaxation mode is characterized by two parameters and the evolution of the disturbance is governed by an augmented Burgers equation. ![]() We consider the case of disturbances propagating in one-dimension through a medium with multiple relaxation modes and thermoviscous diffusion.
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