A Godunov-type tensor artificial viscosity for staggered Lagrangian hydrodynamics

Highlights: • A Godunov type artificial viscosity is derived in tensor space. • The developed viscosity is proved to preserve the cylindrical symmetry. • The developed viscosity performs well in a series of typical cases. This paper describes a tensor artificial viscosity for staggered Lagrangian hydrodynamics. Specifically, two viscous tensors are constructed using a discrete velocity gradient method. Under the condition of a piecewise constant distribution of velocity in each subcell, the Generalized Riemann Invariant relation, in the spirit of the Godunov methods, is applied to determine the coefficients of the viscous tensors. The artificial viscosity is found to be dissipative. Besides, the cylindrical symmetry of the developed artificial viscosity is demonstrated in an equi-angular polar grid. Typical numerical cases with strong shocks show that the tensor artificial viscosity is robust and performs well in different grid types.