Lecture notes for Bulk and Hourglass Viscosities in Wave Propagation Codes

Viscosities, bulk and hourglass, are employed in most finite element and finite difference wave propagation codes and serve two distinct, unrelated functions. Bulk viscosities are used to treat shock waves. Proposed in one spat dimension by von Neumann and Richtmyer in 1950, the bulk viscosity method has since been used by nearly all developers of wave propagation codes. A viscous term, q, added to the pressure, has the effect of smearing shock discontinuities into rapidly varying but continuous transition regions. With this method the solution is unperturbed away from shocks, the Hugoniot jump conditions remain valid across the shock transition, and shocks are automatically treated wherever they arise in the solution. This discussion of bulk viscosity draws heavily on works by Richtmyer and Morton, Noh, and Wilkins.