Discrete equations for physical and numerical compressible multiphase mixtures

By Rémi Abgrall, Richard Saurel. 2003

285 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/e7e18f018c1496b4eca6d963288fc59a44cece99

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

Modelling detonation waves in heterogeneous energetic materials (2004, methodology): “To succeed in this task, the discrete equations method (DEM) of Abgrall and Saurel [2] has been the subject of important extensions: • The averaging method has been revisited and re-interpreted in terms of geometrical averages only.”
Élaboration des lois d'état d'un liquide et de sa vapeur pour les modèles d'écoulements diphasiques Elaborating equations of state of a liquid and its vapor for two-phase flow models (2004, unknown): “Récemment, des choix plus généraux en ce qui concerne les fermetures de ce dernier modèle ont été proposés [10] à l’aide d’une analyse obtenue à partir d’une nouvelle méthode d’homogénéisation [12].”
Solving Irregular and Data-enriched Differential Equations using Deep Neural Networks (2019, background): “A tremendous amount of work spanning pure mathematical analysis [12, 13], numerical analysis [14, 15], physics [16, 17], etc.”
A multiphase model with internal degrees of freedom: application to shock–bubble interaction (2003, methodology): “The methods of Nguyen et al. (2002), Saurel & Abgrall (1999a) and Abgrall & Saurel (2003) guarantee conservation and slip line computation.”
Modelling evaporation fronts with reactive Riemann solvers (2005, methodology): “The discrete equations method (DEM) [ 2 ,29,8] fulfils simultaneously these conditions.”
The Noble-Abel Stiffened-Gas equation of state (2016, background): “Seven-equation models [9–16] are devoted to ﬂows in total disequilibrium.”
Modelling phase transition in metastable liquids: application to cavitating and flashing flows (2008, background): “However, in the general case of finite relaxation rate, the estimates (3.2) are able to enforce interface conditions at each volume fraction discontinuity (equality of normal velocities and pressure) automatically (Abgrall & Saurel 2003).”
Implementation of WENO schemes in compressible multicomponent flow problems (2005, methodology): “The cause of these oscillations is identified in [1], where a quasi-conservative method based on the mass fraction formulation is proposed for gases; subsequently, this has been extended to more general equations of state [39,35,40], and to multiphase [3] and reactive flows [6].”
Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures (2009, background): “Determination of thermodynamic flow variables in these zones is achieved on the basis of multiphase flow theory ([40,4,42,35,3,43,37]).”