On the use of Glimm-like schemes for transport equations on multi-dimensional domain

This paper is dedicated to a numerical method based on Glimm's idea and applied to the specific problem of advection of an indicator function. The numerical scheme relies on a fractional step approach for which: the first step is performed using any classical finite-volume scheme, and the second step sharpens the approximated solution issued from the first step. This second step is based on a random choice as proposed in the original idea of Glimm. In order to assess the capabilities of this approach, several test cases have been investigated including convergence studies with respect to the mesh-size. Since the method proposed in this paper naturally extends to multi-dimensional domain, both one- and two-dimensional cases have been considered

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

International audienceWe 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 two-dimensional numerical simulations of a heated wall are shown and are briefly discussed. Some advantages and weaknesses of algorithms are also discussed

The numerical coupling of a two-fluid model with an homogeneous relaxation model

International audienceWe introduce here some possible way to deal with the unsteady interfacial coupling of two distinct two-phase flow codes. The left code relies on the standard two-fluid approach, and the right code provides approximations of solutions of the Homogeneous Relaxation Model (HRM). The basic idea of the coupling method is to introduce a father model, which corresponds to the two-fluid two-pressure approach, and to define convective fluxes through the interface, once a prolongation of initial conditions on both sides of the coupling interface has been performed. A sketch of the algorithm is provided. More details are given in the paper [HER 06]. A few numerical results show a rather good behaviour of the coupling approach

Coupling two and one-dimensional unsteady Euler equations through a thin interface

International audienceWe present herein a method for the numerical coupling of one and two-dimensional Euler isentropic models through a thin interface. The basic approach is connected with recent works by E. Godlewski, A.Y. Leroux and P.A. Raviart. It requires introducing an interface model, and solving the associated Riemann problem at the interface between codes. Numerical results confirm both the stability and the fair accuracy of the admissible non-conservative approach, which is also compared with an admissible conservative approach and a reference two-dimensional solution. The extension to the full Euler set of equations is also briefly discussed

Assessment of numerical schemes for complex two-phase flows with real equations of state

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A method to couple HEM and HRM two-phase flow models

International audienceWe present a method for the unsteady coupling of two distinct two-phase flow models (namely the Homogeneous Relaxation Model, and the Homogeneous Equilibrium Model) through a thin interface. The basic approach relies on recent works devoted to the inter-facial coupling of CFD models, and thus requires to introduce an interface model. Many numerical test cases enable to investigate the stability of the coupling method

Une classe de modèles diphasiques compressibles

On présente une classe de  modèles d'écoulements diphasiques compressibles pour les simulations instationnaires. L'accent sera mis sur les principes de modélisation retenus pour la fermeture des grandeurs associées à l'interface, notamment les termes de transfert interfacial. On montre que le système fermé est régi par une inégalité d'entropie physique, et qu'il est hyperbolique au sens large. L'impact d'une fermeture particulière sera discuté, ainsi que le respect des conditions de positivité

Adsorption in complex porous networks with geometrical and chemical heterogeneity

International audienceWe report here a simple algorithm to create 2D lattice-based models of porous deposits of preformed nano-metric particles, by mimicking to some extent the physics of the actual deposition/aggregation mechanism. The heterogeneous porous networks obtained exhibit anisotropic properties unlike lattice-based models of porous materials in the existing literature, such as those of porous Vycor glass. We have then used calculations based on the mean field kinetic theory, in order to study the thermodynamics and dynamics of fluid adsorption and desorption in these lattice based porous models. We showcase the influence of pore heterogeneity on the phase equilibrium of the confined fluid, studying both heterogeneity in pore size distribution and chemical heterogeneity of the internal surface

A homogeneous model for compressible three-phase flows involving heat and mass transfer.

A homogeneous model is proposed in order to deal with the simulation of fast transient three-phase ows involving heat and mass transfer. The model accounts for the full thermodynamical disequilibrium between the three phases in terms of pressure, temperature and Gibbs enthalpy. The heat and mass transfer between the phases is modeled in agreement with the second law of thermodynamics, which ensures a stable return to the thermodynamical equilibrium. The set of partial differential equations associated with this model is based on the Euler set of equations supplemented by a complex pressure law, and by six scalar-equations that allow to account for the thermodynamical disequilibrium. It therefore inherits a simple wave structure and possesses important mathematical properties such as: hyperbolicity, unique shock definition through Rankine-Hugoniot relations, positivity of the mixture fractions. Hence the computation of approximated solutions is possible using classical algorithms, which is illustrated by an example of simulation of a steam-explosion