Philippe Helluy

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This paper is devoted to the numerical simulation of wave breaking. It presents the results of a numerical workshop that was held during the conference LOMA04. The objective is to compare several mathematical models (compressible or incompressible) and associated numerical methods to compute the flow field during a wave breaking over a reef. The methods(More)
In this paper we investigate algorithms based on the Fast Legendre Transform (FLT) in order to compute tabulated Equation Of State (EOS) for fluids with phase transition. The equation of state of a binary mixture is given by an energy minimization principle. According to the miscible or immiscible nature of the mixture, the energy of the system is either a(More)
We construct an hyperbolic approximation of the Vlasov equation in which the dependency on the velocity variable is removed. The model is constructed from the Vlasov equation after a Fourier transformation in the velocity variable [9]. A well-chosen nite element semi-discretization in the spectral variable leads to an hyperbolic system.The resulting model(More)
The numerical simulation of compressible two–phase fluid flows exhibits severe difficulties, in particular, when strong variations in the material parameters and high interface velocities are present at the phase boundary. Although several models and discretizations have been developed in the past, a thorough quantitative validation by experimental data and(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)
In this paper we address the problem of solving accurately gas-liquid compressible flows without pressure oscillations at the gas-liquid interface. We introduce a new Lagrange-projection scheme based on a random sampling technique introduced by Chalons and Goatin in [CG07]. We compare it to a ghost fluid approach introduced in [WLK06, MBKKH09] which is(More)
In this paper, we propose a new very simple numerical method for solving liquidgas compressible flows. Such flows are difficult to simulate because classical conservative finite volume schemes generate pressure oscillations at the liquid-gas interface. We extend to several dimensions the random choice scheme that we have constructed in [13]. The extension(More)
We consider a two-fluid compressible flow. Each fluid obeys a stiffened gas pressure law. The continuous model is well defined without considering mixture regions. However, for numerical applications it is often necessary to consider artificial mixtures, because the two-fluid interface is diffused by the numerical scheme. We show that classic pressure law(More)