Shock capturing with PDE-based artificial viscosity for DGFEM: Part I. Formulation

  • Authors:

  • Garrett E. Barter;David L. Darmofal

  • Affiliations:

  • Aerospace Computational Design Laboratory, Massachusetts Institute of Technology, Building 33, Room 207, Cambridge, MA 02139, USA;Aerospace Computational Design Laboratory, Massachusetts Institute of Technology, Building 33, Room 207, Cambridge, MA 02139, USA

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

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Abstract

Artificial viscosity can be combined with a higher-order discontinuous Galerkin finite element discretization to resolve a shock layer within a single cell. However, when a non-smooth artificial viscosity model is employed with an otherwise higher-order approximation, element-to-element variations induce oscillations in state gradients and pollute the downstream flow. To alleviate these difficulties, this work proposes a higher-order, state-based artificial viscosity with an associated governing partial differential equation (PDE). In the governing PDE, a shock indicator acts as a forcing term while grid-based diffusion is added to smooth the resulting artificial viscosity. When applied to heat transfer prediction on unstructured meshes in hypersonic flows, the PDE-based artificial viscosity is less susceptible to errors introduced by grid edges oblique to captured shocks and boundary layers, thereby enabling accurate heat transfer predictions.