A Hybrid Algorithm for the Baer-Nunziato Model Using the Riemann Invariants

Karni, Smadar; Hernández-Dueñas, Gerardo

doi:10.1007/s10915-009-9332-y

Cited by 27 publications

(22 citation statements)

References 14 publications

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“…More specifically, we need to deal with: (1) non-conservative 'nozzling' terms (Schwendeman, Wahle & Kapila 2006;Karni & Hernández-Dueñas 2010;Crochet & Gonthier 2013) arising from variations of the particle volume fraction within a control volume; (2) a pDV work term that affects the gas as particles enter and leave a control volume (Abgrall & Karni 2010);…”

Section: Solution Difficultiesmentioning

confidence: 99%

“…In these cases, refining the grid or using any high-order (therefore more accurate) numerical methods can trigger instabilities that can be masked by excessive numerical diffusion (Nussbaum et al 2006). Recent methods appear to have overcome this for the BN equations (Karni & Hernández-Dueñas 2010;Crochet & Gonthier 2013). Another solution method, used in interior ballistics, is to split the gas and granular conservation equations and solve a Riemann problem for each phase independently and then to compute the non-conservative nozzling and pDV coupling terms separately (Toro 1989), but this approach can violate the non-disturbing condition.…”

Section: Solution Difficultiesmentioning

confidence: 99%

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A multiphase model for compressible granular–gaseous flows: formulation and initial tests

2016

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A model for predicting the behaviour of a compressible flow laden with shocks interacting with granular material has been developed and tested. The model consists of two sets of coupled Euler equations, one for the gas phase and the other for the granular phase. Drag, convective, heat transfer and non-conservative terms couple the two sets of governing equations. Intergranular stress acting on the grains is modelled using granular kinetic theory in dilute regimes where particle collisions are dominant and frictional-collisional pressure in dense regions where layers of granular material slide over one another. The two-phase granular-gaseous model, as a result, is valid from dilute to densely packed granular regimes. The solution of these nonlinearly coupled Euler equations is challenging due to the presence of the non-conservative nozzling and work terms. A numerical technique, based on Godunov's method, was designed for solving these equations. This method takes advantage of particle incompressibility to simplify the nozzling terms. It also uses the observation that a Riemann problem is valid in the region where gas can flow between particles and can be used to provide a physically accurate approximation of the non-conservative terms. The model and solution method are verified by comparisons to test problems involving granular shocks and two-phase shock-tube problems, and they are validated against experimental measurements of shock and dense particle-curtain interactions and transmitted oblique granular shocks.

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Section: Solution Difficultiesmentioning

confidence: 99%

Section: Solution Difficultiesmentioning

confidence: 99%

A multiphase model for compressible granular–gaseous flows: formulation and initial tests

2016

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“…We refer to 10,11,21 for such a description. Of course, other solvers have been proposed for such a purpose, among which we may cite those that are detailed in the papers 1, 2, 7 , which are grounded on the use of relaxation techniques, but also approximate Riemann solvers such as those detailed in 24,26,30,31 . One must be aware here that the approximation of shock solutions makes sense for system (6), though the system has no conservative form, since first-order non-conservative products are only active in linearly degenerate fields.…”

Section: • Relaxation Stepmentioning

confidence: 99%

Computing Two-fluid Models of Compressible Water-vapour Flows with Mass Transfer

Hurisse

2012

42nd AIAA Fluid Dynamics Conference and Exhibit

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“…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.…”

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

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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.

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A Hybrid Algorithm for the Baer-Nunziato Model Using the Riemann Invariants

Cited by 27 publications

References 14 publications

A multiphase model for compressible granular–gaseous flows: formulation and initial tests

A multiphase model for compressible granular–gaseous flows: formulation and initial tests

Computing Two-fluid Models of Compressible Water-vapour Flows with Mass Transfer

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

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