A new form of artificial viscosity

Abstract

An improved form of artificial viscosity results from the substitution of the second Rankine-Hugoniot equation {Δu = [−ΔpΔ( 1 ϱ )] 1 2 } in the equation for q. Thus q = ϱc 2| Δu| 2 becomes q = ϱc 2|Δu [−ΔpΔ( 1 ϱ )] 1 2 . Large velocity gradients (and small pressure gradients) can exist away from shocks, because of geometric effects, and large pressure gradients (and small velocity gradients) can exist in nearly static systems. But if there are both large pressure and velocity gradients, then a shock is present. Thus we see that this form is intrinsically more characteristic of the presence of a shock. Among the several advantages of this form of q, the most important is the improvement in the q heating description as shocks are reflected. Use of the third Rankine-Hugoniot equation in the q is examined, as are some lower-order (linear and 3 2 power) q's.