On positivity-preserving high order discontinuous Galerkin schemes for compressible Navier-Stokes equations

Xiangxiong Zhang Purdue University

Numerical Analysis and Scientific Computing mathscidoc:1701.25005

Journal of Computational Physics, 328, 301–343, 2017
We construct a local Lax-Friedrichs type positivity-preserving flux for compressible Navier-Stokes equations, which can be easily extended to high dimensions for generic forms of equations of state, shear stress tensor and heat flux. With this positivity-preserving flux, any finite volume type schemes including discontinuous Galerkin (DG) schemes with strong stability preserving Runge-Kutta time discretizations satisfy a weak positivity property. With a simple and effi- cient positivity-preserving limiter, high order explicit Runge-Kutta DG schemes are rendered preserving the positivity of density and internal energy without los- ing local conservation or high order accuracy. Numerical tests suggest that the positivity-preserving flux and the positivity-preserving limiter do not induce excessive artificial viscosity, and the high order positivity-preserving DG schemes without other limiters can produce satisfying non-oscillatory solutions when the nonlinear diffusion in compressible Navier-Stokes equations is accurately resolved.
discontinuous Galerkin method, high order accuracy, gas dynamics, compressible Navier-Stokes, positivity-preserving, high speed flows
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@inproceedings{xiangxiong2017on,
  title={On positivity-preserving high order discontinuous Galerkin schemes for compressible Navier-Stokes equations},
  author={Xiangxiong Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170130043340693883135},
  booktitle={Journal of Computational Physics},
  volume={328},
  pages={301–343},
  year={2017},
}
Xiangxiong Zhang. On positivity-preserving high order discontinuous Galerkin schemes for compressible Navier-Stokes equations. 2017. Vol. 328. In Journal of Computational Physics. pp.301–343. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170130043340693883135.
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