An entropy-stable discontinuous Galerkin approximation for the incompressible Navier-Stokes equations with variable density and artificial compressibility

Manzanero Torrico, Juan and Rubio, Gonzalo and Kopriva, David A. and Ferrer, Esteban and Valero, Eusebio (2020). An entropy-stable discontinuous Galerkin approximation for the incompressible Navier-Stokes equations with variable density and artificial compressibility. "Journal of Computational Physics" ; ISSN 0021-9991. https://doi.org/10.1016/j.jcp.2020.109241.

Description

Title: An entropy-stable discontinuous Galerkin approximation for the incompressible Navier-Stokes equations with variable density and artificial compressibility
Author/s:
  • Manzanero Torrico, Juan
  • Rubio, Gonzalo
  • Kopriva, David A.
  • Ferrer, Esteban
  • Valero, Eusebio
Item Type: Article
Título de Revista/Publicación: Journal of Computational Physics
Date: 2020
ISSN: 0021-9991
Subjects:
Faculty: E.T.S. de Ingeniería Aeronáutica y del Espacio (UPM)
Department: Matemática Aplicada a la Ingeniería Aeroespacial
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

We present a provably stable discontinuous Galerkin spectral element method for the incompressible Navier–Stokes equations with artificial compressibility and variable density. Stability proofs, which include boundary conditions, that follow a continuous entropy analysis are provided. We define a mathematical entropy function that combines the traditional kinetic energy and an additional energy term for the artificial compressibility, and derive its associated entropy conservation law. The latter allows us to construct a provably stable split–form nodal Discontinuous Galerkin (DG) approximation that satisfies the summation–by–parts simultaneous–approximation–term (SBP–SAT) property. The scheme and the stability proof are presented for general curvilinear three–dimensional hexahedral meshes. We use the exact Riemann solver and the Bassi–Rebay 1 (BR1) scheme at the inter–element boundaries for inviscid and viscous fluxes respectively, and an explicit low storage Runge–Kutta RK3 scheme to integrate in time. We assess the accuracy and robustness of the method by solving a manufactured solution, the Kovasznay flow, a lid driven cavity, the inviscid Taylor–Green vortex, and the Rayleigh–Taylor instability.

Funding Projects

TypeCodeAcronymLeaderTitle
Horizon 2020H2020-CS2-CFP06-2017-01UnspecifiedUnspecifiedUnspecified

More information

Item ID: 60425
DC Identifier: https://oa.upm.es/60425/
OAI Identifier: oai:oa.upm.es:60425
DOI: 10.1016/j.jcp.2020.109241
Official URL: https://www.sciencedirect.com/science/article/pii/S0021999120300152?via%3Dihub
Deposited by: Memoria Investigacion
Deposited on: 18 Jan 2022 12:22
Last Modified: 19 Jan 2022 10:28
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