A note on finite-scale Navier–Stokes theory: The case of constant viscosity, strictly adiabatic flow

We investigate the “piston problem” for the case of a viscous, but non-thermally conducting, gas with constant transport coefficients under the recently introduced generalization of the Navier–Stokes (NS) equations known as the finite-scale Navier–Stokes (FSNS) equations. Along with determining and analyzing the integral curves of the resulting kink-type traveling wave solutions (TWS)s, the present study also reveals the importance of the bulk viscosity vis-a-vis this special case of FSNS theory and highlights the impact that averaging has on the structure of the shock profile.