Shock wave structure in a strongly nonlinear lattice with viscous dissipation

Shock wave structure in a lattice gas

The motion and structure of shock and expansion waves in a simple particle system, a lattice gas and cellular automaton, are determined in an exact computation. Shock wave solutions, also exact, of a continuum description, a model Boltzmann equation, are compared with the lattice results. The comparison demonstrates that, as proved by Caprino et al. “A derivation of the Broadwell equation,” Com...

Singular Nonlinear Boundary Value Problems Arising in Viscous Flow Behind a Shock Wave

A rigorous proof for existence and uniqueness of solutions to a class of singular nonlinear boundary value problems arising in viscous flow and heat transfer behind a shock wave is made and a theoretical estimate formula for the skin friction coefficient is presented. The formula can be successfully applied to estimate the value of the skin friction coefficient. The correctness of the analytica...

Nonlinear stability of viscous shock wave to one-dimensional compressible isentropic Navier-Stokes equations with density dependent viscous coefficient

We prove nonlinear stability of viscous shock wave of arbitrary amplitudes to a one-dimensional compressible isentropic Navier-Stokes equations with density dependent viscosity. Under the assumption that the viscous coefficient is given as a power function of density, any viscous shock wave is shown to be nonlinear stable for small initial perturbations with integral zero. In contrast to previo...

Proper formulation of viscous dissipation for nonlinear waves in solids.

To model nonlinear viscous dissipative motions in solids, acoustical physicists usually add terms linear in Ė, the material time derivative of the Lagrangian strain tensor E, to the elastic stress tensor σ derived from the expansion to the third (sometimes fourth) order of the strain energy density E=E(tr E,tr E(2),tr E(3)). Here it is shown that this practice, which has been widely used in the...

Nonlinear Stability of Viscous Shock Waves