A simple stabilized finite element method for solving two phase compressible–incompressible interface flows

Billaud, M.; Gallice, Gérard; Nkonga, Boniface

doi:10.1016/j.cma.2010.10.017

Cited by 21 publications

(17 citation statements)

References 38 publications

(116 reference statements)

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“…In order to express all the previous relations in terms of the primitive variables alone, we make the supposition that the fluid is divariant and account for the ideal gas law. This makes possible to formulate density as a function of the pressure and the temperature, and to rearrange the Navier-Stokes equations (see [11,30]). Hence, the Jacobian matrices A j (Y) , j = 0, .…”

Section: Compressible Navier-stokes Equations Written In Primitive Vamentioning

confidence: 99%

“…Some authors (e.g. [10,11]) tried to design τ matrices that were suitable for both the low Mach number limit and high Mach number flows. A necessary requirement for those matrices is the a priori knowledge of numerical parameters depending on the compressibility of the flow.…”

Section: The Matrix τ Of Stabilization Parametersmentioning

confidence: 99%

“…For more details on entropy variable formulations we refer to [9,10]. In the case of the compressible Navier-Stokes equations written in primitive variables, the formulation simplifies to the incompressible equations when the incompressible constraint is included (as explained in [11]), and consequently, it is well defined in the low Mach number limit.…”

Section: Introductionmentioning

confidence: 99%

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Solution of low Mach number aeroacoustic flows using a Variational Multi-Scale finite element formulation of the compressible Navier–Stokes equations written in primitive variables

Ballon-Bayona

Baiges

Codina

2019

Computer Methods in Applied Mechanics and Engineering

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In this work we solve the compressible Navier-Stokes equations written in primitive variables in order to simulate low Mach number aeroacoustic flows. We develop a Variational Multi-Scale formulation to stabilize the finite element discretization by including the orthogonal, dynamic and non-linear subscales, together with an implicit scheme for advancing in time. Three additional features define the proposed numerical scheme: the splitting of the pressure and temperature variables into a relative and a reference part, the definition of the matrix of stabilization parameters in terms of a modified velocity that accounts for the local compressibility, and the approximation of the dynamic stabilization matrix for the time dependent subscales. We also include a weak imposition of implicit non-reflecting boundary conditions in order to overcome the challenges that arise in the aeroacoustic simulations at low compressibility regimes. The order of accuracy of the method is verified for two-and three-dimensional linear and quadratic elements using steady manufactured solutions. Several benchmark flow problems are studied, including transient examples and aeroacoustic applications. c

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Section: Compressible Navier-stokes Equations Written In Primitive Vamentioning

confidence: 99%

Section: The Matrix τ Of Stabilization Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Solution of low Mach number aeroacoustic flows using a Variational Multi-Scale finite element formulation of the compressible Navier–Stokes equations written in primitive variables

Ballon-Bayona

Baiges

Codina

2019

Computer Methods in Applied Mechanics and Engineering

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“…The most used common problem is the study of rising bubbles in a conductive medium. This problem, classical in the CFD literature (Billaud et al , 2011; Bhaga and Weber, 1981; Hachem et al , 2016), has gained relevance in the MHD community (Jin et al , 2016) because it is a basic phenomenon happening in casting of steel (Pavlovs et al , 2016; Tatulcenkovs et al , 2016) and boiling phenomena (Kamiyama and Ishimoto, 1995). A second advanced CFD benchmark is the model of a falling droplet: MHD studies of this problem (Wang et al , 2014; Zhang and Ni, 2014) have been adding to the pure fluid mechanics results obtained in the past decade (Nvan Hinsberg et al , 2010; Xue et al , 2007; Berberovic et al , 2009).…”

Section: Introductionmentioning

confidence: 99%

Two-fluid flow under the constraint of external magnetic field

Marioni

Khalloufi

Bay

et al. 2017

HFF

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International audiencePurpose - This paper aims to develop a robust set of advanced numerical tools to simulate multiphase flows under the superimposition of external uniform magnetic fields. Design/methodology/approach - The flow has been simulated in a fully Eulerian framework by a {\it variational multi-scale} method, which allows to take into account the small-scale turbulence without explicitly model it. The multi-fluid problem has been solved through the convectively re-initialized level-set method to robustly deal with high density and viscosity ratio between the phases and the surface tension has been modelled implicitly in the level-set framework. The interaction with the magnetic field has been modelled through the classic induction equation for 2D problems and the time step computation is based on the electromagnetic interaction to guarantee convergence of the method. Anisotropic mesh adaptation is then used to adapt the mesh to the main problem's variables and to reach good accuracy with a small number of degrees of freedom. Finally, the variational multiscale method leads to a natural stabilization of the finite elements algorithm, preventing numerical spurious oscillations in the solution of Navier-Stokes equations (fluidmechanics) and the transport equation (level-set convection). Findings - The methodology has been validated, and it is shown to produce accurate results also with a low number of degrees of freedom. The physical effect of the external magnetic field on the multiphase flow has been analysed. Originality/value - The dam-break benchmark case has been extended to include magnetically constrained flow

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“…Note that, another model is to treat the problem using a two-phase model in which the governing equations are the same, see for example [2,6,10,11,13,15,16,36,37,39,41,42,44,46,47]. There are advantages and limitations for each model.…”

Section: Introductionmentioning

confidence: 99%

A semi-implicit augmented IIM for Navier–Stokes equations with open, traction, or free boundary conditions

Xiao

Cai

et al. 2015

Journal of Computational Physics

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In this paper, a new Navier–Stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open, traction, and free boundary conditions, which can be applied to simulations of fluid structure interaction, implicit solvent model for biomolecular applications and other free boundary or interface problems. For some problems of this type, the projection method and the augmented immersed interface method (IIM) do not work well or does not work at all. The proposed new Navier–Stokes solver is based on the local pressure boundary method, and a semi-implicit augmented IIM. A fast Poisson solver can be used in our algorithm which gives us the potential for developing fast overall solvers in the future. The time discretization is based on a second order multi-step method. Numerical tests with exact solutions are presented to validate the accuracy of the method. Application to fluid structure interaction between an incompressible fluid and a compressible gas bubble is also presented.

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A simple stabilized finite element method for solving two phase compressible–incompressible interface flows

Cited by 21 publications

References 38 publications

Solution of low Mach number aeroacoustic flows using a Variational Multi-Scale finite element formulation of the compressible Navier–Stokes equations written in primitive variables

Solution of low Mach number aeroacoustic flows using a Variational Multi-Scale finite element formulation of the compressible Navier–Stokes equations written in primitive variables

Two-fluid flow under the constraint of external magnetic field

A semi-implicit augmented IIM for Navier–Stokes equations with open, traction, or free boundary conditions

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