Papers by Philippe Helluy
Computers Fluids, Oct 1, 2009
The numerical simulation of compressible two-phase fluid flows exhibits severe difficulties, in p... 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 a detailed comparison of numerical schemes are hardly available.
C R Acad Sci Ser I Math, 1998
In several papers of Bouchut, Bourdarias, Perthame and Coquel, Le Floch ((13), (7)...), a general... more In several papers of Bouchut, Bourdarias, Perthame and Coquel, Le Floch ((13), (7)...), a general methodology has been developed to construct second order flnite volume schemes for hyperbolic systems of conservation laws satisfying the entire family of entropy inequalities. This approach is mainly based on the construction of an entropy diminishing projection. Unfor- tunately, the explicit computation of this projection
Proceedings of the 3rd International Workshop on OpenCL - IWOCL '15, 2015
We introduce in this paper a well-balanced approximate Riemann solver in order to compute Euler e... more We introduce in this paper a well-balanced approximate Riemann solver in order to compute Euler equations in one-dimensional variable cross section geometries. The scheme takes its roots on the early ideas of Greenberg and Leroux. In order to avoid expensive exact Riemann solvers through cell interfaces, the VFRoe-ncv approximate Godunov scheme is applied, while focusing on a specific change of variable. This choice preserves non-trivial steady states on any mesh size. Details on the scheme and its properties are exhibited, and numerical results are presented afterwards.
Journal of Computational and Applied Mathematics
A well-balanced approximate Riemann solver is introduced in this paper in order to compute approx... more A well-balanced approximate Riemann solver is introduced in this paper in order to compute approximations of one-dimensional Euler equations in variable cross-section ducts. The interface Riemann solver is grounded on VFRoe-ncv scheme, and it enforces the preservation of Riemann invariants of the steady wave. The main properties of the scheme are detailed. We provide numerical results to assess the validity of the scheme, even when the cross section is discontinuous. A first series is devoted to analytical test cases, and the last results correspond to the simulation of a bubble collapse.
In this report, we address several aspects of the approximation of the MHD equations by a Galerki... more In this report, we address several aspects of the approximation of the MHD equations by a Galerkin Discontinuous finite volume schemes. This work has been initiated during a CEMRACS project in july and august 2008 in Luminy. The project was entitled GADMHD (for GAlerkin Discontinuous approximation for the Magneto-Hydro-Dynamics). It has been supported by the INRIA CALVI project.
This work is devoted to the numerical modelling of a reactive gas- particle ∞ow that arises in in... more This work is devoted to the numerical modelling of a reactive gas- particle ∞ow that arises in internal ballistic. The model, proposed by Gough (1), takes into account complex physical phenomena such as mass transfer, drag force or intra granular stress. A non-conservative flnite volume approach adapted from (10) is applied in order to simulate the model. After an academic
Springer Proceedings in Mathematics, 2011
... Journal of Computational Physics 227, 25142539 (2008) 6. Fox, RO, Laurent, F.,Massot, M.: Nu... more ... Journal of Computational Physics 227, 25142539 (2008) 6. Fox, RO, Laurent, F.,Massot, M.: Numerical simulation of spray coalescence in an Eulerian framework: direct quadrature method of moments and multi-fluid method. ...
ESAIM: Proceedings, 2012
Numerical simulations of complete hydraulic systems (e.g. diesel injectors) can, due to high comp... more Numerical simulations of complete hydraulic systems (e.g. diesel injectors) can, due to high computational costs, currently not be done entirely in three dimensions. Our aim is to substitute the 3D solver by a corresponding 1D method in some parts of the system and develop a solver coupling with suitable interface models. Firstly, we investigate an interface model for non-cavitating flow passing the interface. A flux-coupling with a thin interface approach is considered and the jump in dimensions at the interface is transferred to an additional variable φ, which switches between the 3D and the 1D domain. As shown in two testcases, the error introduced in the vicinity of the interface is quite small. Two numerical flux formulations for the flux over the 3D-1D interface are compared and the Roe-type flux formulation is recommended. Secondly, extending the first method to cavitating flows passing the interface, we divide the density equation in two equations -one for liquid and one for vapor phase of the two-phase fluid -and couple the two equations by source terms depending on the free enthalpy. We propose two interface models for coupling 3D and 1D compressible density-based Euler methods that have potential for considering the entire (non-) cavitating hydraulic system behaviour by a 1D method in combination with an embedded detailed 3D simulation at much lower computational costs than the pure 3D simulation.
ESAIM: Proceedings and Surveys, 2014
Theoretical and Computational Acoustics 2003 - The Sixth International Conference (ICTCA), 2004
The adjoint model method of control theory is known to give accurate and efficient data assimilat... more The adjoint model method of control theory is known to give accurate and efficient data assimilation processes in oceanography and meteorology. However, it has rarely been applied in underwater acoustics for inversion purposes. Based on the back-propagation of the mismatch between observations and their predictions, the adjoint model can produce the corrections to the associated direct forward model input parameters. In this paper, the adjoint of a parabolic equation propagation model with non local impedance boundary conditions at the water sediment interface is used in order to determine an acoustically equivalent representation of the seabed. The bottom is represented by these boundary conditions that play the role of the control parameter.
Theory, Numerics and Applications(In 2 Volumes), 2012
ABSTRACT We propose a numerical method to model the dynamical behavior of a spherical bubble of v... more ABSTRACT We propose a numerical method to model the dynamical behavior of a spherical bubble of vapor and air inside water. The air is assumed to be miscible with the vapor. Each phase is described by a stiffened gas law and the mixture pressure law is recovered by an entropy maximization process. We use an adaptive finite volume solver in order to solve the Euler equations. Numerical experiments are presented that validate our approach.
ESAIM: Proceedings and Surveys, 2014
ESAIM: Proceedings, 2013
We give in this paper a short review of some recent achievements within the framework of multipha... more We give in this paper a short review of some recent achievements within the framework of multiphase flow modeling. We focus first on a class of compressible two-phase flow models, detailing closure laws and their main properties. Next we briefly summarize some attempts to model two-phase flows in a porous region, and also a class of compressible three-phase flow models. Some of the main difficulties arising in the numerical simulation of solutions of these complex and highly non-linear systems of PDEs are then discussed, and we eventually show some numerical results when tackling twophase flows with mass transfer.
Multiphase Science and Technology, 2004
The two-layer laminar Poiseuille flow is suggested as a case test. Two superimposed layers of vis... more The two-layer laminar Poiseuille flow is suggested as a case test. Two superimposed layers of viscous fluids separated by a flat interface are flowing in a horizontal channels. The analytical solution is provided.
39th AIAA Thermophysics Conference, 2007
This work is devoted to the numerical modeling of multi-dimensional reactive gasparticle flows in... more This work is devoted to the numerical modeling of multi-dimensional reactive gasparticle flows in a gun. We consider 2D or 3D flows in ducts of variable section. Not only complex physical phenomenons are taken into account such as interphase mass and energy transfer, but complex geometries too. Our mathematical model 2 is only conditionally hyperbolic. We thus propose a fractional step method where each step is proved to be hyperbolic. The whole system is solved by a non-conservative finite volume method, adapted from 5 . Validations are made on academic shock tube problems and then on several interior ballistic experiments.
We present a two-fluid hyperbolic model in order to compute gas-particle flows that are highly lo... more We present a two-fluid hyperbolic model in order to compute gas-particle flows that are highly loaded with particles. The classical Baer-Nunziato model is modified in order to take into account the compaction of the solid phase. All closure laws for drag effects, mass and energy transfer terms are in agreement with the entropy inequality. Due to the possible compaction, the pressure relaxation terms differ from their counterparts in the dilute case. We proposed a fractional step method that complies with the entropy inequality. Special emphasis is given here on the case of an instantaneous pressure relaxation step. Our algorithm guarantees that the volume fraction remains within its bounds. A few numerical results are presented on coarse and fine meshes. Other results are available in [CAR 07, NUS 07].
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Papers by Philippe Helluy