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Hybrid central-upwind schemes for numerical resolution of two-phase flows

Steinar Evje, Tore Flåtten (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper we present a methodology for constructing accurate and efficient hybrid central-upwind (HCU) type schemes for the numerical resolution of a two-fluid model commonly used by the nuclear and petroleum industry. Particularly, we propose a method which does not make use of any information about the eigenstructure of the jacobian matrix of the model. The two-fluid model possesses a highly nonlinear pressure law. From the mass conservation equations we develop an evolution equation which...

Hybrid central-upwind schemes for numerical resolution of two-phase flows

Steinar Evje, Tore Flåtten (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we present a methodology for constructing accurate and efficient hybrid central-upwind (HCU) type schemes for the numerical resolution of a two-fluid model commonly used by the nuclear and petroleum industry. Particularly, we propose a method which does not make use of any information about the eigenstructure of the Jacobian matrix of the model. The two-fluid model possesses a highly nonlinear pressure law. From the mass conservation equations we develop an evolution equation which...

Hybrid finite volume scheme for a two-phase flow in heterogeneous porous media*

Konstantin Brenner (2012)

ESAIM: Proceedings

We propose a finite volume method on general meshes for the numerical simulation of an incompressible and immiscible two-phase flow in porous media. We consider the case that can be written as a coupled system involving a degenerate parabolic convection-diffusion equation for the saturation together with a uniformly elliptic equation for the global pressure. The numerical scheme, which is implicit in time, allows computations in the case of a heterogeneous...

Hybrid model for the Coupling of an Asymptotic Preserving scheme with the Asymptotic Limit model: The One Dimensional Case⋆

Pierre Degond, Fabrice Deluzet, Dario Maldarella, Jacek Narski, Claudia Negulescu, Martin Parisot (2011)

ESAIM: Proceedings

In this paper a strategy is investigated for the spatial coupling of an asymptotic preserving scheme with the asymptotic limit model, associated to a singularly perturbed, highly anisotropic, elliptic problem. This coupling strategy appears to be very advantageous as compared with the numerical discretization of the initial singular perturbation model or the purely asymptotic preserving scheme introduced in previous works [3, 5]. The model problem addressed...

Hydrodynamics of Inelastic Maxwell Models

V. Garzó, A. Santos (2011)

Mathematical Modelling of Natural Phenomena

An overview of recent results pertaining to the hydrodynamic description (both Newtonian and non-Newtonian) of granular gases described by the Boltzmann equation for inelastic Maxwell models is presented. The use of this mathematical model allows us to get exact results for different problems. First, the Navier–Stokes constitutive equations with explicit expressions for the corresponding transport coefficients are derived by applying the Chapman–Enskog...

Hydromagnetic stability of stratified shear flows in the presence of cross flow

Naresh Kumar Dua, Hari Kishan, Ruchi Goel (2011)

Annales Polonici Mathematici

The hydromagnetic stability of stratified shear flows in the presence of cross flows is discussed. The magnetic field is applied in the direction of the main flow. Some necessary conditions of instability, the growth rate of unstable modes and reduction of the unstable region are discussed.

Hyperbolic relaxation models for granular flows

Thierry Gallouët, Philippe Helluy, Jean-Marc Hérard, Julien Nussbaum (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this work we describe an efficient model for the simulation of a two-phase flow made of a gas and a granular solid. The starting point is the two-velocity two-pressure model of Baer and Nunziato [Int. J. Multiph. Flow16 (1986) 861–889]. The model is supplemented by a relaxation source term in order to take into account the pressure equilibrium between the two phases and the granular stress in the solid phase. We show that the relaxation process can be made thermodynamically coherent with an...

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