A fully conservative and shift-invariant formulation for Galerkin discretizations of incompressible variable density flow

This paper introduces a formulation of the variable density incompressible Navier-Stokes equations by modifying the nonlinear terms in a consistent way. For Galerkin discretizations, the formulation leads to favorable discrete conservation properties without the divergence-free constraint being stro...

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Veröffentlicht in:Journal of computational physics Jg. 510; S. 113086
Hauptverfasser: Lundgren, Lukas, Nazarov, Murtazo
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.08.2024
Schlagworte:
Beräkningsvetenskap med inriktning mot numerisk analys
Conservation
EMAC formulation
Incompressible variable density flow
Navier-Stokes equations
Navier-Stokes equations Conservation
Scientific Computing with specialization in Numerical Analysis
Structure-preserving discretization
Viscous regularization
Viscous regularization
Incompressible variable density flow
Structure-preserving discretization
EMAC formulation
Conservation
Navier-Stokes equations
ISSN:0021-9991, 1090-2716
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Zusammenfassung:This paper introduces a formulation of the variable density incompressible Navier-Stokes equations by modifying the nonlinear terms in a consistent way. For Galerkin discretizations, the formulation leads to favorable discrete conservation properties without the divergence-free constraint being strongly enforced. In addition, the formulation is shown to make the density field invariant to global shifts. The effect of viscous regularizations on conservation properties is also investigated. Numerical tests validate the theory developed in this work. The new formulation shows superior performance compared to other formulations from the literature, both in terms of accuracy for smooth problems and in terms of robustness. •A new formulation for variable density incompressible flow is introduced.•The formulation leads to improved conservation properties without the divergence-free being strongly enforced.•The effect of viscous regularization on conservation properties is investigated.•Conservation of mass, kinetic energy, squared density, momentum and angular momentum are analyzed.•Mass is conserved by matching or reducing the polynomial degree of density to that of pressure.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2024.113086