The viscous part of the pressure tensor is Newtonian: The thermal and viscous parts of the First-Law energy change are then apportioned between the x and y directions so as to be consistent with overall energy conservation: The thermal relaxation time τ has been introduced in the evolution equations to guarantee thermal equilibrium far from the shockwave: In what follows we consider two models for the cold curve and the heat capacity. First, a weak repulsive pair force suggests implementing a “van der Waals model”: Second, a triangular-lattice-based model, based on Gr¨ uneisen’s ideas, uses the nearest- neighbor static lattice energy and pressure corresponding to the pair potential evaluated at the nearest-neighbor lattice spacing r , φ = (10 /π )(1 − r ) $^{3}$: The corresponding equilibrium equation of state separates the energy and pressure into “cold” and “thermal” parts: with γ chosen so as to roughly reproduce equation of state data from molecular dynamics. Let us next apply these two simple cold-curve models to the shockwave problem. P viscous = − λ ∇ · uI − η ( ∇ u + ∇ u $^{t}$) . ˙ e thermal = ˙ e − ˙ e $^{cold}$( ρ ) = ck ˙ T$_{xx}$ + ck ˙ T$_{yy}$ ; ρck ˙ T$_{xx}$ = − α ∇ u : ( P − IP $^{cold}$) − β ∇ · Q + ρck ( T$_{yy}$ − T$_{xx}$ ) /τ ; ρck ˙ T$_{yy}$ = ( α − 1) ∇ u : ( P − IP $^{cold}$) + ( β − 1) ∇ · Q + ρck ( T$_{xx}$ − T$_{yy}$ ) /τ . K$_{x}$ = K$_{y}$ ↔ T$_{xx}$ = T$_{yy}$ = T eq . e cold = ( ρ/ 2) ; e thermal = k ( T$_{xx}$ + T$_{yy}$ ) / 2 ; P eq = ρe e cold = (30 /π )(1 − r ) 3 ; p $^{cold}$( V/N ) = (45 /π ) r (1 − r ) 2 ; r = √ V/V$_{0}$ ; V$_{0}$ = √ 3 / 4 N . e eq = e cold + e thermal ; P eq = P cold + ργe thermal ,