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A discrete kinetic energy preserving convection operator for variable density flows on locally refined staggered meshes

Abstract : In this paper, we build and analyze a scheme for the time-dependent variable density Navier-Stokes equations, able to cope with unstructured non-conforming meshes, with hanging nodes. The time advancement relies on a pressure correction algorithm and the space approximation is based on a low-order staggered non-conforming finite element, the so-called Rannacher-Turek element. The convection term in the momentum balance equation is discretized by a finite volume technique, and a careful construction of the fluxes, especially through non-conforming faces, ensures that the solution obeys a discrete kinetic energy balance. Its consistency is addressed by analyzing a model problem, namely the convection-diffusion equation, for which we theoretically establish a first order convergence in space for energy norms. This convergence order is also observed in the numerical experiments for the Navier-Stokes equations. Navier-Stokes equations, pressure correction scheme, finite volumes, finite elements, stability, kinetic energy, non-conforming local refinement.
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https://hal.archives-ouvertes.fr/hal-02391939
Contributor : Khaled Saleh <>
Submitted on : Tuesday, December 3, 2019 - 5:38:03 PM
Last modification on : Thursday, March 5, 2020 - 3:29:48 PM
Document(s) archivé(s) le : Wednesday, March 4, 2020 - 8:24:05 PM

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  • HAL Id : hal-02391939, version 1

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J.-C Latché, B Piar, Khaled Saleh. A discrete kinetic energy preserving convection operator for variable density flows on locally refined staggered meshes. 2019. ⟨hal-02391939⟩

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