A framework for developing a mimetic tensor artificial viscosity for Lagrangian hydrocodes on arbitrary polygonal meshes

We construct a new mimetic tensor artificial viscosity on general polygonal meshes. The tensor artificial viscosity is based on discretization of coordinate invariant operators, divergence of a tensor and gradient of a vector. The focus of this paper is on the non-symmetric form, div( μ∇ u), of the tensor artificial viscosity. The discretizations of this operator is derived for the case of a full tensor coefficient μ. However, in the numerical experiments, we only use scalar μ. We prove that the new tensor viscosity preserves spatial symmetry on special meshes. We demonstrate performance of the new viscosity for the Noh implosion, Sedov explosion and Saltzman piston problems on a set of various polygonal meshes in both Cartesian and axisymmetric coordinate systems.