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

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• 作者：Xiangxiong Zhang ^{zhan1966@purdue.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Discontinuous Galerkin method ; High order accuracy ; Gas dynamics ; Compressible Navier&ndash ; Stokes ; Positivity-preserving ; High speed flows
• 刊名：Journal of Computational Physics
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：328
• 期：Complete
• 页码：301-343
• 全文大小：6990 K

文摘

We construct a local Lax–Friedrichs type positivity-preserving flux for compressible Navier–Stokes equations, which can be easily extended to multiple 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 efficient positivity-preserving limiter, high order explicit Runge–Kutta DG schemes are rendered preserving the positivity of density and internal energy without losing 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.