MINJEAUD , Sebastian

In this article, we propose to study two issues associated with the use of the incremental projection method for solving the incompressible Navier-Stokes equation. The first one is the combination of this time splitting algorithm with an adaptive local refinement method. The second one is the reduction of spurious velocities due to the...

We propose an original scheme for the time discretization of a triphasic Cahn- Hilliard/Navier-Stokes model. This scheme allows an uncoupled resolution of the discrete Cahn-Hilliard and Navier-Stokes system, is unconditionally stable and preserves, at the discrete level, the main properties of the continuous model. The existence of discrete...

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We address the Korteweg-de Vries equation as an interesting model of high order partial differential equation, and show that it is possible to develop reliable and effective schemes, in terms of accuracy, computational efficiency, simplicity of implementation and, if required, conservation of the lower invariants, on the basis of a (only)...

In this paper, we introduce a specific modification of the numerical fluxes in order to insure the well-balanced property of schemes on staggered grids for the Euler equations. This property is crucial for the numerical representation of equilibrium solutions of balance laws with source terms, like when describing flows subjected to gravity and...

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In this paper, we introduce a specific modification of the numerical fluxes in order to insure the well-balanced property of schemes on staggered grids for the Euler equations. This property is crucial for the numerical representation of equilibrium solutions of balance laws with source terms, like when describing flows subjected to gravity and...

International audience

International audience

International audience

In this paper, we propose a new generalization of the well-known Cahn-Hilliard two-phase model for the modelling of n-phase mixtures. The model is derived using the consistency principle: we require that our n-phase model exactly coincide with the classical two-phase model when only two phases are present in the system. We give conditions for...

Hyperbolic systems and dispersive equations remain challenging for the FEM community. Onthe basis of an arbitrarily high order FEM, namely the spectral element method (SEM), here weaddress:- The Korteweg-de Vries equation, to explain how high order derivative terms can be efficientlyhandled with a C 0 continuous Galerkin...

In this paper, we propose a new generalization of the well-known Cahn-Hilliard two-phase model for the modelling of n-phase mixtures. The model is derived using the consistency principle: we require that our n-phase model exactly coincide with the classical two-phase model when only two phases are present in the system. We give conditions for...

To address the so-called Bohm boundary conditions, generally imposed at the walls that intercept in a tokamak the magnetic field lines, we consider a simple one-dimensional hyperbolic system that constitutes a minimal transport model for ionic density and momentum. We show that as soon as the solution is smooth, a spectrally accurate...

Due to the extreme conditions required to produce energy by nuclear fusion in tokamaks, simulating the plasma behavior is an important but challenging task. We focus on the edge part of the plasma, where fluid approaches are probably the best suited, and our approach relies on the Braginskii ion–electron model. Assuming that the electric field...

We present a second order scheme for the barotropic and full Euler equations. The scheme works on staggered grids, with numerical unknowns stored at dual locations, while the numerical fluxes are derived in the spirit of kinetic schemes. We identify stability conditions ensuring the positivity of the discrete density and energy. We illustrate...

Il existe, sous la surface de nos océans, un immense réseau de courants marins, véritables tapis roulants des mers, qui transportent des masses d'eau absolument gigantesques. Ces courants à grande échelle, parmi lesquels figure le célèbre Gulf Stream, jouent un rôle primordial dans la dynamique des océans, et bien entendu dans l'équilibre...

We present a new scheme for the simulation of the barotropic Euler equation in low Mach regimes. The method uses two main ingredients. First, the system is treated with a suitable time splitting strategy, directly inspired from [J. Haack, S. Jin, J.-G. Liu, Comm. Comput. Phys., 12 (2012) 955-980], that separates low and fast waves. Second, we...

The Capillary Equation correctly predicts the curvature evolution and the length of a quasi-static vapour formation. It describes a two-phase interface as a smooth curve resulting from a balance of curvatures that are influenced by surface tension and hydrostatic pressures. The present work provides insight into the application of the Capillary...

We introduce muscl reconstructions for schemes designed on staggered grids for the numerical resolution of the Euler system. The proposed scheme uses principles based on the Discrete Duality Finite Volume framework for which the structure of the unknowns makes the gradient reconstruction naturally amenable. Dealing with general unstructured...

We investigate a fluid modeling approach to describe the plasma behavior in tokamaks. For the numerical approximation, we use a high order method based on Fourier expansions in the toroidal direction and the spectral element method (SEM) in the poloidal plane. We first focus on anisotropic diffusion, because in tokamaks diffusion strongly...

Il existe, sous la surface de nos océans, un immense réseau de courants marins, véritables tapis roulants des mers, qui transportent des masses d'eau absolument gigantesques. Ces courants à grande échelle, parmi lesquels figure le célèbre Gulf Stream, jouent un rôle primordial dans la dynamique des océans, et bien entendu dans l'équilibre...

We set up a MUSCL approach for the 2D DDFV-like scheme introduced in [Goudon, Llobell, Minjeaud, 2022] for the full Euler equations, discretized with unstructured meshes. It is a finite volume staggered discretization framework where numerical densities, energies and velocities are stored on different locations. For the MUSCL scheme, a...

We propose a numerical scheme for the simulation of fluid-particles flows with two incompressible phases. The numerical strategy is based on a finite volume discretization on staggered grids, with a flavor of kinetic schemes in the definition of the numerical fluxes. We particularly pay attention to the difficulties related to the volume...

Il existe, sous la surface de nos océans, un immense réseau de courants marins, sortes de tapis roulants des mers, qui transportent des masses d'eau absolument gigantesques. Ces courants à grande échelle, parmi lesquels figure le célèbre Gulf Stream, jouent un rôle primordial dans la dynamique des océans, et bien entendu dans l'équilibre...