Jean-Marc Hérard

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The present paper is devoted to the computation of two-phase flows using the two-fluid approach. The overall model is hyperbolic and has no conservative form. No instantaneous local equilibrium between phases is assumed, which results in a two-velocity twopressure model. Original closure laws for interfacial velocity and interfacial pressure are proposed.(More)
We present here a three-fluid three-pressure model to describe three-field patterns or three-phase flows. The basic ideas rely on the counterpart of the two-fluid two-pressure model which has been introduced in the DDT (deflagration to detonation theory) framework, and has been more recently extended to liquid–vapour simulations. We first show that the(More)
A method to solve the Navier–Stokes equations for incompressible viscous flows and the convection and diffusion of a scalar is proposed in the present paper. This method is based upon a fractional time step scheme and the finite volume method on unstructured meshes. A recently proposed diffusion scheme with interesting theoretical and numerical properties(More)
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(More)
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(More)
We provide herein some ways to compute flashing flows in variable cross section ducts, focusing on the Homogeneous Relaxation Model. The basic numerical method relies on a splitting technique which is consistent with the overall entropy inequality. The cross section is assumed to be continuous, and the Finite Volume approach is applied to approximate(More)
This paper is devoted to the comparison of three two-fluid models in steam-water applications involving phase transition and shock waves. The three models are presented in a common formalism that helps to underline their shared properties. A numerical method based on previous work is extended to all models and to more complex Equations Of State. Particular(More)
We present a relaxation scheme for approximating the entropy dissipating weak solutions of the BaerNunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in [16] for the isentropic Baer-Nunziato model and consequently inherits its main properties. Up to our knowledge, this is the(More)