A dissipation model for staggered grid Lagrangian hydrodynamics
Viscosity terms are explicitly added to the Lagrangian staggered grid hydrodynamic equations for calculating shock wave problems. The explicit viscosity terms are commonly termed artificial viscosity. All shocks are irreversible so a dissipation model is necessary to capture the entropy created by a shock. In this work, viscosity models are derived via analytic solutions to one-dimensional shock problems for materials having linear and non-linear relationships between particle velocity and shock velocity. The dissipation model includes linear, quadratic, and cubic viscosity terms. The linear viscosity term is used to damp spurious oscillations, whereas, the quadratic and cubic viscosities are used to capture the pressure difference between a shock wave and an acoustic wave. The quadratic and cubic viscosity coefficients are material dependent and are calculated using fits to experimental data. The details of the viscosity model are discussed and numerical tests are presented. (C) 2012 Elsevier Ltd. All rights reserved.
dissipation lagrangian hydrodynamics viscosity