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

  • Authors:

  • K. Lipnikov;M. Shashkov

  • Affiliations:

  • Los Alamos National Laboratory, MS B284, Los Alamos, NM 87545, United States;Los Alamos National Laboratory, MS B284, Los Alamos, NM 87545, United States

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2010

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Abstract

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(@m@?u), of the tensor artificial viscosity. The discretizations of this operator is derived for the case of a full tensor coefficient @m. However, in the numerical experiments, we only use scalar @m. 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.