Khaled Saleh

Bio: Khaled Saleh is an academic researcher from Claude Bernard University Lyon 1. The author has contributed to research in topics: Finite volume method & Discretization. The author has an hindex of 8, co-authored 26 publications receiving 223 citations. Previous affiliations of Khaled Saleh include Institut de radioprotection et de sûreté nucléaire & University of Lyon.

A Robust Entropy-Satisfying Finite Volume Scheme for the Isentropic Baer-Nunziato Model

Abstract: We construct an approximate Riemann solver for the isentropic Baer−Nunziato two-phase flow model, that is able to cope with arbitrarily small values of the statistical phase fractions The solver relies on a relaxation approximation of the model for which the Riemann problem is exactly solved for subsonic relative speeds In an original manner, the Riemann solutions to the linearly degenerate relaxation system are allowed to dissipate the total energy in the vanishing phase regimes, thereby enforcing the robustness and stability of the method in the limits of small phase fractions The scheme is proved to satisfy a discrete entropy inequality and to preserve positive values of the statistical fractions and densities The numerical simulations show a much higher precision and a more reduced computational cost (for comparable accuracy) than standard numerical schemes used in the nuclear industry Finally, two test-cases assess the good behavior of the scheme when approximating vanishing phase solutions

Two properties of two-velocity two-pressure models for two-phase flows

Abstract: We study a class of models of compressible two-phase flows. This class, which includes the Baer-Nunziato model, is based on the assumption that each phase is described by its own pressure, velocity and temperature and on the use of void fractions obtained from averaging process. These models are nonconservative and non-strictly hyperbolic. We prove that the mixture entropy is non-strictly convex and that the system admits a symmetric form.

A Robust and Entropy-Satisfying Numerical Scheme for Fluid Flows in Discontinuous Nozzles

Abstract: We propose in this work an original finite volume scheme for the system of gas dynamics in a nozzle. Our numerical method is based on a piecewise constant discretization of the cross-section and on an approximate Riemann solver in the sense of Harten, Lax and van Leer. The solver is obtained by the use of a relaxation approximation that leads to a positive and entropy satisfying numerical scheme for all variation of section, even discontinuous sections with arbitrary large jumps. To do so, we introduce, in the first step of the relaxation solver, a singular dissipation measure superposed on the standing wave, which enables us to control the approximate speeds of sound and thus the time step, even for extreme initial data.

Analyse et Simulation Numérique par Relaxation d'Ecoulements Diphasiques Compressibles. Contribution au Traitement des Phases Evanescentes.

Abstract: Cette these s'interesse au modele diphasique de Baer-Nunziato. L'objectif de ce travail est de proposer quelques techniques de prise en compte de la disparition de phase, regime occasionnant d'importantes instabilites au niveau du modele et de sa simulation numerique. Par des methodes d'analyse et de simulation reposant sur les techniques d'approximation par relaxation a la Suliciu, on montre que dans ces regimes, on peut stabiliser les solutions en introduisant une dissipation de l'entropie totale de melange. Dans une premiere approche dite approche Eulerienne directe, la resolution exacte du probleme de Riemann pour le systeme relaxe permet de definir un schema entropique extremement precis, et qui se revele bien plus economique en terme de cout CPU (a precision donnee) que le schema classique tres simple de Rusanov. De plus, nous montrons que ce schema permet de simuler avec robustesse des regimes de disparition de phase. Le schema est developpe en 1D puis etendu en 3D et integre a un prototype de code industriel developpe par EDF. La deuxieme approche, dite approche par splitting acoustique, propose une separation des ondes acoustiques rapides et des ondes de transport lentes. L'objectif est d'eviter la resonance due a l'interaction entre ces deux types d'ondes, et de permettre a long terme un traitement implicite de l'acoustique, et explicite du transport. Le schema, tres simple, permet la prise en compte simple de la disparition de phase. La nouveaute est ici l'exploitation de fermetures dissipatives nouvelles du couple vitesse et pression d'interface, qui permettent le controle des solutions du probleme de Riemann associe a l'etape acoustique.

A well-balanced scheme to capture non-explicit steady states in the Euler equations with gravity

Abstract: Summary This paper describes a numerical discretization of the compressible Euler equations with a gravitational potential. A pertinent feature of the solutions to these inhomogeneous equations is the special case of stationary solutions with zero velocity, described by a nonlinear partial differential equation, whose solutions are called hydrostatic equilibria. We present a well-balanced method, meaning that besides discretizing the complete equations, the method is also able to maintain all hydrostatic equilibria. The method is a finite volume method, whose Riemann solver is approximated by a so-called relaxation Riemann solution that takes all hydrostatic equilibria into account. Relaxation ensures robustness, accuracy, and stability of our method, because it satisfies discrete entropy inequalities. We will present numerical examples, illustrating that our method works as promised. Copyright © 2015 John Wiley & Sons, Ltd.

A Robust Entropy-Satisfying Finite Volume Scheme for the Isentropic Baer-Nunziato Model

Abstract: We construct an approximate Riemann solver for the isentropic Baer−Nunziato two-phase flow model, that is able to cope with arbitrarily small values of the statistical phase fractions The solver relies on a relaxation approximation of the model for which the Riemann problem is exactly solved for subsonic relative speeds In an original manner, the Riemann solutions to the linearly degenerate relaxation system are allowed to dissipate the total energy in the vanishing phase regimes, thereby enforcing the robustness and stability of the method in the limits of small phase fractions The scheme is proved to satisfy a discrete entropy inequality and to preserve positive values of the statistical fractions and densities The numerical simulations show a much higher precision and a more reduced computational cost (for comparable accuracy) than standard numerical schemes used in the nuclear industry Finally, two test-cases assess the good behavior of the scheme when approximating vanishing phase solutions

Closure conditions for non-equilibrium multi-component models

Abstract: A class of non-equilibrium models for compressible multi-component fluids in multi-dimensions is investigated taking into account viscosity and heat conduction. These models are subject to the choice of interfacial pressures and interfacial velocity as well as relaxation terms for velocity, pressure, temperature and chemical potentials. Sufficient conditions are derived for these quantities that ensure meaningful physical properties such as a non-negative entropy production, thermodynamical stability, Galilean invariance and mathematical properties such as hyperbolicity, subcharacteristic property and existence of an entropy–entropy flux pair. For the relaxation of chemical potentials, a two-component and a three-component models for vapor–water and gas–water–vapor, respectively, are considered.

Long‐term adaptive response to high‐frequency light signals in the unicellular photosynthetic eukaryote Dunaliella salina

Abstract: Productivity of microalgal cultivation processes is tightly related to photosynthetic efficiency, and therefore to light availability at the cell scale. In an agitated, highly turbid suspension,the light signal received by a single phytoplankton cell moving in a dense culture is a succession of flashes. The growth characteristics of microalgae under such dynamic light conditions are thus fundamental information to understand nonlinear properties of the photosynthetic process and to improve cultivation process design and operation. Studies of the long term consequences of dynamic illumination regime on photosynthesis require a very specific experimental set-up where fast varying signals are applied on the long term. In order to investigate the growth response of the unicellular photosynthetic eukaryote Dunaliella salina (Chlorophyceae) to intermittent light exposure, different light regimes using LEDs with the same average total light dose were applied in continuous cultures. Flashing light with different durations of light flashes (△t of 30 s, 15 s, 2 s and 0.1 s) followed by dark periods of variable length (0.67 ≤ L:D ≤ 2) yielding flash frequencies in the range 0.017–5 Hz, were compared to continuous illumination. Specific growth rate, photosynthetic pigments, lipid productivity and elemental composition were measured on two duplicates for each irradiance condition. The different treatments of intermittent light led to specific growth rates ranging from 0.25 to 0.93 day−1. While photosynthetic efficiency was enhanced with increased flash frequency, no significant differences were observed in the particular carbon and chlorophyll content. Pigment analysis showed that within this range of flash frequency, cells progressively photoacclimated to the average light intensity. Biotechnol. Bioeng. 2015;112: 1111–1121. © 2015 Wiley Periodicals, Inc.