Hyperbolic relaxation models for granular flows

Gallouët, Thierry; Helluy, Philippe; Hérard, Jean-Marc; Nussbaum, Julien

doi:10.1051/m2an/2010006

Cited by 24 publications

(31 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The interfacial transfer contributions have been studied in [4,5,17,10,28,29], and a summary can be found in appendix A. These terms are thus defined as:…”

Section: Closure Laws For Interfacial Transfer Termsmentioning

confidence: 99%

“…The same procedure provides some way to tackle the modeling of three-phase flows [18] . It also gives a relevant approach for the modeling of dense granular flows [10] . These extensions confirm the relevance of the whole modeling approach.…”

Section: Introductionmentioning

confidence: 99%

“…The most difficult task dwells in the building of suitable algorithms in the pressure relaxation step. Of course this difficulty vanishes when the pressure relaxation time scale is set to zero, but in that case convergence difficulties -with respect to the mesh size-may be expected (see [21,17,10]) when focusing on unsteady computations. The first section of numerical results focuses on the practical estimation of the rate of convergence when looking for approximate solutions of the convective subset.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A fractional step method to compute a class of compressible gas–liquid flows

Hérard¹,

Hurisse²

2012

Computers & Fluids

Self Cite

View full text Add to dashboard Cite

We present in this paper some algorithms dedicated to the computation of numerical approximations of a class of two-fluid two-phase flow models. Governing equations for the statistical void fraction, partial mass, momentum, energy are presented first, and meaningful closure laws are given. Then we may give the main properties of the class of two-fluid models. The whole algorithm that relies on the fractional step method and complies with the entropy inequality is presented afterwards. Emphasis is given on the computation of pressure-velocity-temperature relaxation source terms. Conditions pertaining to the existence and uniqueness of discrete solutions of the relaxation step are given. While focusing on some one-dimensional test cases, the true rates of convergence may be obtained within the evolution step and the relaxation step. Eventually, some twodimensional numerical simulations of a heated wall are shown and are briefly discussed. Some advantages and weaknesses of algorithms are also discussed.

show abstract

“…The interfacial transfer contributions have been studied in [4,5,17,10,28,29], and a summary can be found in appendix A. These terms are thus defined as:…”

Section: Closure Laws For Interfacial Transfer Termsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A fractional step method to compute a class of compressible gas–liquid flows

Hérard¹,

Hurisse²

2012

Computers & Fluids

Self Cite

View full text Add to dashboard Cite

show abstract

“…Some algorithms have been proposed in [10,17] for that purpose. The celerity of acoustic waves in the pure liquid (respectively vapour) phase is noted c l (resp.…”

Section: Governing Equations Of the Baer-nunziato Modelmentioning

confidence: 99%

“…then scheme (10), (11), (12) preserves positive values of partial masses m φ and void fractions α φ , for φ = l, v.…”

Section: Numerical Schemesmentioning

confidence: 99%

Approximate solutions of the Baer-Nunziato Model

Crouzet

Daude²,

Helluy

et al. 2013

ESAIM: Proc.

Self Cite

View full text Add to dashboard Cite

Abstract. We examine in this paper the accuracy of some approximations of the BaerNunziato two-phase flow model. The governing equations and their main properties are recalled, and two distinct numerical schemes are investigated, including a classical secondorder extension relying on symmetrizing variables. Shock tube cases are considered, and two simple Riemann problems based on well-balanced initial data are detailed. These enable to recover the expected convergence rates. However, it is shown that these simple cases are indeed very difficult and that the accuracy of basic schemes is rather poor.Résumé. Approximation des solutions du modèle de Baer-Nunziato On examine ici la précision des approximations obtenues pour le modèle diphasique de BaerNunziato. Leséquations du modèle et ses principales propriétés sont rappellées. Deux schémas distincts sont proposés, et des extensions classiques au second-ordre sont considérées, utilisant les variables de symétrisation. Des cas tests de tubeà choc sont analysés, notamment deux cas utilisant des conditions initiales enéquilibre. Les taux de convergence attendus sont retrouvés, mais on montre que la précision des approximations de certains problèmes de Riemann est assez médiocre.

show abstract

Finite Volume Methods: Foundation and Analysis

Barth

Herbin

Ohlberger

2017

Encyclopedia of Computational Mechanics Second Edition

View full text Add to dashboard Cite

Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems. They are extensively used in fluid mechanics, porous media flow, meteorology, electromagnetics, models of biological processes, semi-conductor device simulation and many other engineering areas governed by conservative systems that can be written in integral control volume form.This article reviews elements of the foundation and analysis of modern finite volume methods.The primary advantages of these methods are numerical robustness through the obtention of discrete maximum (minimum) principles, applicability on very general unstructured meshes, and the intrinsic local conservation properties of the resulting schemes. Throughout this article, specific attention is given to scalar nonlinear hyperbolic conservation laws and the development of high order accurate schemes for discretizing them. A key tool in the design and analysis of finite volume schemes suitable for non-oscillatory discontinuity capturing is discrete maximum principle analysis. A number of building blocks used in the development of numerical schemes possessing local discrete maximum principles are reviewed in one and several space dimensions, e.g. monotone fluxes, E-fluxes, TVD discretization, nonoscillatory reconstruction, slope limiters, positive coefficient schemes, etc. When available, theoretical results concerning a priori and a posteriori error estimates are given. Further advanced topics are then considered such as high order time integration, discretization of dffision terms and the extension to systems of nonlinear conservation laws.

show abstract

Hyperbolic relaxation models for granular flows

Cited by 24 publications

References 14 publications

A fractional step method to compute a class of compressible gas–liquid flows

A fractional step method to compute a class of compressible gas–liquid flows

Approximate solutions of the Baer-Nunziato Model

Finite Volume Methods: Foundation and Analysis

Contact Info

Product

Resources

About