Numerical approximation for a Baer–Nunziato model of two-phase flows

Thanh, Mai Duc; Kröner, Dietmar; Nam, Nguyen Thanh

doi:10.1016/j.apnum.2011.01.004

Cited by 23 publications

(14 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Observe that the results similar to (2.15) and (2.16) were obtained in [2,10,34] for an alternative model of two-phase flows, where the compaction dynamics is given under another form. The quantities in the gas phase can be found using (2.15).…”

Section: Jump Relations and The Change Of Volume Fractionsupporting

confidence: 68%

See 1 more Smart Citation

Well-Balanced Roe-Type Numerical Scheme for a Model of Two-Phase Compressible Flows

Thanh¹

2014

Journal of the Korean Mathematical Society

Self Cite

View full text Add to dashboard Cite

Abstract. We present a multi-stage Roe-type numerical scheme for a model of two-phase flows arisen from the modeling of deflagration-todetonation transition in granular materials. The first stage in the construction of the scheme computes the volume fraction at every time step. The second stage deals with the nonconservative terms in the governing equations which produces states on both side of the contact wave at each node. In the third stage, a Roe matrix for the two-phase is used to apply on the states obtained from the second stage. This scheme is shown to capture stationary waves and preserves the positivity of the volume fractions. Finally, we present numerical tests which all indicate that the proposed scheme can give very good approximations to the exact solution.

show abstract

Section: Jump Relations and The Change Of Volume Fractionsupporting

confidence: 68%

“…The reader is referred to [1,11,16,20,24,25] for numerical schemes for multi-phase multi-pressure models. In [33,34], well-balanced numerical schemes for two-phase flow models were built by using stationary waves to track the source terms. Well-balanced numerical schemes for one-pressure models of two-phase flows were constructed in [30,31].…”

Section: 1)mentioning

confidence: 99%

Well-Balanced Roe-Type Numerical Scheme for a Model of Two-Phase Compressible Flows

Thanh¹

2014

Journal of the Korean Mathematical Society

Self Cite

View full text Add to dashboard Cite

show abstract

“…We refer to [5,6,7,16,18] for a single conservation law with source term and to [22,23,25,24] for fluid flows in a nozzle with variable cross-section. Well-balanced schemes for multi-phase flows and other models were studied in [2,9,36,38].…”

Section: Introductionmentioning

confidence: 99%

A Godunov-type method for the shallow water equations with discontinuous topography in the resonant regime

LeFloch

Thanh²

2011

Journal of Computational Physics

Self Cite

103

View full text Add to dashboard Cite

We investigate the Riemann problem for the shallow water equations with variable and (possibly) discontinuous topography and provide a complete description of the properties of its solutions: existence; uniqueness in the non-resonant regime; multiple solutions in the resonant regime. This analysis leads us to a numerical algorithm that provides one with a Riemann solver. Next, we introduce a Godunov-type scheme based on this Riemann solver, which is well-balanced and of quasi-conservative form. Finally, we present numerical experiments which demonstrate the convergence of the proposed scheme even in the resonance regime, except in the limiting situation when Riemann data precisely belong to the resonance hypersurface.

show abstract

“…Note that, to our knowledge, there exists no solver that is able to capture exactly a moving contact discontinuity on coarse meshes, and our scheme compares rather well with other schemes (see [13]). Nevertheless, the method proposed in [16] exactly captures stationary contacts, i.e. contacts with u 2 = 0.…”

Section: Test Case 1: a Contact Discontinuitymentioning

confidence: 99%

“…For other approaches relying on different assumptions, see [4,14]. Several schemes have already been proposed in the literature in order to build consistent and stable approximations of the Baer-Nunziato model, among which we may cite those relying on interface Riemann solvers (see for instance [12,[15][16][17]) and other schemes relying on relaxation techniques (see for instance [1]). …”

Section: Introductionmentioning

confidence: 99%

A splitting method for the isentropic Baer-Nunziato two-phase flow model

Coquel

Hérard²,

Saleh

2012

ESAIM: Proc.

View full text Add to dashboard Cite

Abstract. In the present work, we propose a fractional step method for computing approximate solutions of the isentropic Baer-Nunziato two-phase flow model. The scheme relies on an operator splitting method corresponding to a separate treatment of fast propagation phenomena due to the acoustic waves on the one hand and slow propagation phenomena due to the fluid motion on the other. The scheme is proved to preserve positive values of the statistical fractions and densities. We also provide two test-cases that assess the convergence of the method.Résumé. Nous proposons ici une méthodeà pas fractionnaires pour le calcul de solutions approchées pour la version isentropique du modèle diphasique de Baer-Nunziato. Le schéma s'appuie sur un splitting de l'opérateur temporel correspondantà la prise en compte différenciée des phéno-mènes de propagation rapide dus aux ondes acoustiques et des phénomènes de propagation lente dus aux ondes matérielles. On prouve que le schéma permet de préserver des valeurs positives pour les taux statistiques de présence des phases ainsi que pour les densités. Deux cas tests numériques permettent d'illustrer la convergence de la méthode.

show abstract

Numerical approximation for a Baer–Nunziato model of two-phase flows

Cited by 23 publications

References 29 publications

Well-Balanced Roe-Type Numerical Scheme for a Model of Two-Phase Compressible Flows

Well-Balanced Roe-Type Numerical Scheme for a Model of Two-Phase Compressible Flows

A Godunov-type method for the shallow water equations with discontinuous topography in the resonant regime

A splitting method for the isentropic Baer-Nunziato two-phase flow model

Contact Info

Product

Resources

About