Shock waves in a one-dimensional non-dissipating lattice

Abstract

A one-dimensional lattice model is studied for shock wave propagation. Two types of non-linear nearest neighbour interactions are considered. Numerical solutions of the resulting differential-difference equations of motion are described. Computations yield values of steady particle velocity which agree with predictions of the Rankine-Hugoniot jump conditions for a continuum; shock velocities exceed those predicted by the jump conditions by as much as 6%.