Entropy stable modal discontinuous Galerkin schemes and wall boundary conditions for the compressible Navier-Stokes equations

Chan, Jesse; Lin, Yimin; Warburton, Tim

doi:10.1016/j.jcp.2021.110723

Title: Entropy stable modal discontinuous Galerkin schemes and wall boundary conditions for the compressible Navier-Stokes equations

Journal Article · Tue Sep 21 00:00:00 EDT 2021 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2021.110723· OSTI ID:1977270

Chan, Jesse ^[1]; Lin, Yimin ^[1]; Warburton, Tim ^[2]

Rice University, Houston, TX (United States)
Virginia Polytechnic Inst. and State University (Virginia Tech), Blacksburg, VA (United States)

Entropy stable schemes ensure that physically meaningful numerical solutions also satisfy a semi-discrete entropy inequality under appropriate boundary conditions. Here in this work, we describe a discretization of viscous terms in the compressible Navier-Stokes equations which enables a simple and explicit imposition of entropy stable no-slip and reflective (symmetry) wall boundary conditions for discontinuous Galerkin (DG) discretizations. Specifically, we derive methods for imposing adiabatic no-slip and reflective (symmetry) boundary conditions for modal entropy stable DG formulations which preserve a semi-discrete entropy inequality. Numerical results confirm the robustness and accuracy of the proposed approaches.

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Research Organization:: Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

Sponsoring Organization:: USDOE Office of Science (SC); USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)

Grant/Contract Number:: SC0023471

OSTI ID:: 1977270

Journal Information:: Journal of Computational Physics, Vol. 448, Issue C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Title: Entropy stable modal discontinuous Galerkin schemes and wall boundary conditions for the compressible Navier-Stokes equations

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