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.

本文描述了交错拉格朗日流体动力学的张量人工粘度。具体地，使用离散速度梯度方法构造两个粘性张量。在每个子像元中速度呈分段恒定分布的条件下，按照Godunov方法的精神，使用广义Riemann不变关系来确定粘性张量的系数。发现人造粘度是耗散的。此外，在等角极性网格中证明了所开发的人工粘度的圆柱对称性。具有强烈冲击的典型数值案例表明，张量人工粘度很强，并且在不同的网格类型中表现良好。