This paper briefly presents the research activity of our group on the coupling problem of differe... more This paper briefly presents the research activity of our group on the coupling problem of different partial differential equations (PDE) at a fixed interface. Our motiva- tion comes from the coupling of different two-phase flow codes that involve different PDE systems for simulating the components of a nuclear reactor.
We prove the existence and uniqueness,of the Riemann,solutions to the Euler equations closed by N... more We prove the existence and uniqueness,of the Riemann,solutions to the Euler equations closed by N independent,constitutive pressure laws. This model,stands as a natural asymptotic system,for the multi-pressure Navier-Stokes equations in the regime of infinite Reynolds number. Due to the inherent lack of conservation form in the viscous regularization, the limit system exhibits measure-valued,source terms concentrated,on shock discontinuities. These non-positive
We study the asymptotic behavior of the solutions of barotropic two-phase two-pressure models, wi... more We study the asymptotic behavior of the solutions of barotropic two-phase two-pressure models, with pressure relaxation, drag force and external forces. Using Chapman-Enskog expansions close to the expected equilibrium, a drift-flux model with a Darcy type closure law is obtained. Also, restricting this closure law to permanent flows (defined as steady flows in some Lagrangian frame), we can obtain a
We investigate the existence and properties of traveling wave solutions for the hyperbolic-ellipt... more We investigate the existence and properties of traveling wave solutions for the hyperbolic-elliptic system of conservation laws describing the dynamics of van der Waals fluids. The model is based on a constitutive equation of state containing two inflection points and incorporates nonlinear viscosity and capillarity terms. A global description of the traveling wave solutions is provided. We distinguish between classical
ABSTRACT A new version of Godunov’s scheme is proposed to compute the solutions of a traffic flow... more ABSTRACT A new version of Godunov’s scheme is proposed to compute the solutions of a traffic flow model with phase transitions. The scheme is based on a modified averaging strategy and a sampling procedure.
When modelling and simulating complex systems, one often needs to use specific models for each co... more When modelling and simulating complex systems, one often needs to use specific models for each com- ponent to take into account their behavior. This is the case, for instance, for the modelling of the coolant flow in a Pressurized Water Reactor. In the frame of the NEPTUNE project, it is clear that to obtain a complete and coherent description of
We study two separate domains sharing a fixed interface. In ea ch one, a different hy- perbolic m... more We study two separate domains sharing a fixed interface. In ea ch one, a different hy- perbolic model is used to describe the flow. We propose approp riate conditions at the interface in a way to obtain a coherent description of the unsteady flow a ccording to physical considera- tions. The problem we consider is the coupling of the homogen
This paper reports investigations on the computation of material fronts in multi-fluid models usi... more This paper reports investigations on the computation of material fronts in multi-fluid models using a Lagrange-Projection approach. Various forms of the Projection step are considered. Particular attention is paid to minimization of conservation errors.
ABSTRACT This work considers the numerical approximation of the shallow-water equations. In this ... more ABSTRACT This work considers the numerical approximation of the shallow-water equations. In this context, one faces three important issues related to the well-balanced, positivity and entropy-preserving properties, as well as the ability to consider vacuum states. We propose a Godunov-type method based on the design of a three-wave Approximate Riemann Solver (ARS) which satisfies the first two properties and a weak form of the last one together. Regarding the entropy, the solver satisfies a discrete non-conservative entropy inequality. From a numerical point of view, we also investigate the validity of a conservative entropy inequality.
We consider the seven-equation model for compressible two-phase flows and propose a large time-st... more We consider the seven-equation model for compressible two-phase flows and propose a large time-step numerical scheme based on a time implicit-explicit Lagrange-Projection strategy introduced in Coquel et al. [6] for Euler equations. The main objective is to get a Courant-Friedrichs-Lewy (CFL) condition driven by (slow) contact waves instead of (fast) acoustic waves.
This paper briefly presents the research activity of our group on the coupling problem of differe... more This paper briefly presents the research activity of our group on the coupling problem of different partial differential equations (PDE) at a fixed interface. Our motiva- tion comes from the coupling of different two-phase flow codes that involve different PDE systems for simulating the components of a nuclear reactor.
We prove the existence and uniqueness,of the Riemann,solutions to the Euler equations closed by N... more We prove the existence and uniqueness,of the Riemann,solutions to the Euler equations closed by N independent,constitutive pressure laws. This model,stands as a natural asymptotic system,for the multi-pressure Navier-Stokes equations in the regime of infinite Reynolds number. Due to the inherent lack of conservation form in the viscous regularization, the limit system exhibits measure-valued,source terms concentrated,on shock discontinuities. These non-positive
We study the asymptotic behavior of the solutions of barotropic two-phase two-pressure models, wi... more We study the asymptotic behavior of the solutions of barotropic two-phase two-pressure models, with pressure relaxation, drag force and external forces. Using Chapman-Enskog expansions close to the expected equilibrium, a drift-flux model with a Darcy type closure law is obtained. Also, restricting this closure law to permanent flows (defined as steady flows in some Lagrangian frame), we can obtain a
We investigate the existence and properties of traveling wave solutions for the hyperbolic-ellipt... more We investigate the existence and properties of traveling wave solutions for the hyperbolic-elliptic system of conservation laws describing the dynamics of van der Waals fluids. The model is based on a constitutive equation of state containing two inflection points and incorporates nonlinear viscosity and capillarity terms. A global description of the traveling wave solutions is provided. We distinguish between classical
ABSTRACT A new version of Godunov’s scheme is proposed to compute the solutions of a traffic flow... more ABSTRACT A new version of Godunov’s scheme is proposed to compute the solutions of a traffic flow model with phase transitions. The scheme is based on a modified averaging strategy and a sampling procedure.
When modelling and simulating complex systems, one often needs to use specific models for each co... more When modelling and simulating complex systems, one often needs to use specific models for each com- ponent to take into account their behavior. This is the case, for instance, for the modelling of the coolant flow in a Pressurized Water Reactor. In the frame of the NEPTUNE project, it is clear that to obtain a complete and coherent description of
We study two separate domains sharing a fixed interface. In ea ch one, a different hy- perbolic m... more We study two separate domains sharing a fixed interface. In ea ch one, a different hy- perbolic model is used to describe the flow. We propose approp riate conditions at the interface in a way to obtain a coherent description of the unsteady flow a ccording to physical considera- tions. The problem we consider is the coupling of the homogen
This paper reports investigations on the computation of material fronts in multi-fluid models usi... more This paper reports investigations on the computation of material fronts in multi-fluid models using a Lagrange-Projection approach. Various forms of the Projection step are considered. Particular attention is paid to minimization of conservation errors.
ABSTRACT This work considers the numerical approximation of the shallow-water equations. In this ... more ABSTRACT This work considers the numerical approximation of the shallow-water equations. In this context, one faces three important issues related to the well-balanced, positivity and entropy-preserving properties, as well as the ability to consider vacuum states. We propose a Godunov-type method based on the design of a three-wave Approximate Riemann Solver (ARS) which satisfies the first two properties and a weak form of the last one together. Regarding the entropy, the solver satisfies a discrete non-conservative entropy inequality. From a numerical point of view, we also investigate the validity of a conservative entropy inequality.
We consider the seven-equation model for compressible two-phase flows and propose a large time-st... more We consider the seven-equation model for compressible two-phase flows and propose a large time-step numerical scheme based on a time implicit-explicit Lagrange-Projection strategy introduced in Coquel et al. [6] for Euler equations. The main objective is to get a Courant-Friedrichs-Lewy (CFL) condition driven by (slow) contact waves instead of (fast) acoustic waves.
Uploads
Papers by Christophe Chalons