The Riemann problem for the nonisentropic Baer–Nunziato model of two-phase flows

Thanh, Mai Duc; Vinh, Duong Xuan

doi:10.1016/j.nonrwa.2022.103623

Cited by 3 publications

(4 citation statements)

References 26 publications

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“…It also seems worth mentioning the recent Discontinuous Galerkin scheme described in [17]. Eventually, we point out the recent work [62] dedicated to the analysis of the Riemann problem associated with the Baer-Nunziato model.…”

Section: Finite Volume Techniques To Compute System (5)mentioning

confidence: 85%

Two approaches to compute unsteady compressible two-phase flow models with stiff relaxation terms

Hérard,

Jomée

2023

ESAIM: M2AN

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The paper deals with the numerical modeling of two-phase flows while using Baer-Nunziato type models. Focus is given here on the numerical treatment of source terms that involve three (or four) relaxation time scales. A new coupled approach relying on the continuous analysis of the system of ODEs is compared with a more widely used strategy grounded on the fractional step approach. Properties of schemes are given in both cases. Several numerical applications show that the coupled approach should be prefered for both stability and accuracy reasons.

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Section: Finite Volume Techniques To Compute System (5)mentioning

confidence: 85%

Two approaches to compute unsteady compressible two-phase flow models with stiff relaxation terms

Hérard,

Jomée

2023

ESAIM: M2AN

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“…[23][24][25][26][27][28] The Riemann problem for the model (1.1) were considered in Thanh and Vinh. 29 See also other studies [30][31][32] and the references therein.…”

Section: Introductionmentioning

confidence: 97%

“…The Riemann problem for two‐phase flow models was studied in previous research 23–28 . The Riemann problem for the model () were considered in Thanh and Vinh 29 . See also other studies 30–32 and the references therein.…”

Section: Introductionmentioning

confidence: 99%

The minimum entropy principle for a two‐phase flow model

Thanh

Vinh

2022

Math Methods in App Sciences

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Bounded entropy solutions of the Baer-Nunziato model of two-phase flows are proved to satisfy the minimum entropy principle; that is, the spatial infimum of the specific entropy inf x S(u(x, t)) is an increasing function of time. The model was derived for the study of deflagration-to-detonation transition in granular explosives and consists of seven nonlinear partial differential equations with nonconservative source terms. Apparently, we will also show that the generalized entropy inequality can be reduced in the usual divergence form for standard entropy pairs in gas dynamics equations.

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“…Opanasenko et al 26 explored generalized symmetries, conservation laws, and Hamiltonian structures of an isothermal no‐slip DFM. Mathematical analysis of coupling conditions of the vertex flow for no‐slip drift‐flux case of multiphase flows was established by Banda et al 27 Analyzing the Riemann problem for various models we refer References 28‐32. Furthermore, different equations of state are introduced to find the solutions of DFM.…”

Section: Introductionmentioning

confidence: 99%

Solution to the Riemann problem for drift‐flux model with modified Chaplygin two‐phase flows

Zeidan

Jana

Kuila

et al. 2022

Numerical Methods in Fluids

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In this paper, we concern about the Riemann problem for compressible no‐slip drift‐flux model which represents a system of quasi‐linear partial differential equations derived by averaging the mass and momentum conservation laws with modified Chaplygin two‐phase flows. We obtain the exact solution of Riemann problem by elaborately analyzing characteristic fields and discuss the elementary waves namely, shock wave, rarefaction wave and contact discontinuity wave. By employing the equality of pressure and velocity across the middle characteristic field, two nonlinear algebraic equations with two unknowns as gas density ahead and behind the middle wave are formed. The Newton–Raphson method of two variables is applied to find the unknowns with a series of initial data from the literature. Finally, the exact solution for the physical quantities such as gas density, liquid density, velocity, and pressure are illustrated graphically.

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The Riemann problem for the nonisentropic Baer–Nunziato model of two-phase flows

Cited by 3 publications

References 26 publications

Two approaches to compute unsteady compressible two-phase flow models with stiff relaxation terms

Two approaches to compute unsteady compressible two-phase flow models with stiff relaxation terms

The minimum entropy principle for a two‐phase flow model

Solution to the Riemann problem for drift‐flux model with modified Chaplygin two‐phase flows

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