A conservative finite element method for the incompressible Euler equations with variable density

JOURNAL OF COMPUTATIONAL PHYSICS

卷:412

Article

Gawlik, Evan S.¹  Gay-Balmaz, Francois² 

[1] Univ Hawaii Manoa, Dept Math, Honolulu, HI 96822 USA

[2] CNRS, LMD, Ecole Normale Super, Paris, France

关键词: Finite element;    Energy-conserving;    Incompressible flow;    Variable density;    Inviscid;    Exactly divergence-free;   

DOI  :  10.1016/j.jcp.2020.109439

来源: Elsevier

【 摘 要 】

We construct a finite element discretization and time-stepping scheme for the incompressible Euler equations with variable density that exactly preserves total mass, total squared density, total energy, and pointwise incompressibility. The method uses Raviart-Thomas or Brezzi-Douglas-Marini finite elements to approximate the velocity and discontinuous polynomials to approximate the density and pressure. To achieve exact preservation of the aforementioned conserved quantities, we exploit a seldom-used weak formulation of the momentum equation and a second-order time-stepping scheme that is similar, but not identical, to the midpoint rule. We also describe and prove stability of an upwinded version of the method. We present numerical examples that demonstrate the order of convergence of the method. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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