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

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 i...

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Bibliographic Details
Published in:Journal of computational physics 2010-03, Vol.229 (5), p.1810-1827
Main Authors: Barter, Garrett E., Darmofal, David L.
Format: Article
Language:English
Subjects:
Artificial viscosity
Compressible Navier–Stokes
Computational techniques
Discontinuous Galerkin
Exact sciences and technology
Mathematical methods in physics
Physics
Shock capturing
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Summary: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.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2009.11.010