Boundary value problems for the stationary Vlasov-Maxwell system.
Boussinesq/Boussinesq systems for internal waves with a free surface, and the KdV approximation
We study here some asymptotic models for the propagation of internal and surface waves in a two-fluid system. We focus on the so-called long wave regime for one-dimensional waves, and consider the case of a flat bottom. Following the method presented in [J.L. Bona, T. Colin and D. Lannes, Arch. Ration. Mech. Anal. 178 (2005) 373–410] for the one-layer case, we introduce a new family of symmetric hyperbolic models, that are equivalent to the classical Boussinesq/Boussinesq system displayed in [W. Choi...
Boussinesq/Boussinesq systems for internal waves with a free surface, and the KdV approximation
We study here some asymptotic models for the propagation of internal and surface waves in a two-fluid system. We focus on the so-called long wave regime for one-dimensional waves, and consider the case of a flat bottom. Following the method presented in [J.L. Bona, T. Colin and D. Lannes, Arch. Ration. Mech. Anal.178 (2005) 373–410] for the one-layer case, we introduce a new family of symmetric hyperbolic models, that are equivalent to the classical Boussinesq/Boussinesq system displayed in [W. Choi...
Branching process associated with 2d-Navier Stokes equation.
Ω being a bounded open set in R∙, with regular boundary, we associate with Navier-Stokes equation in Ω where the velocity is null on ∂Ω, a non-linear branching process (Yt, t ≥ 0). More precisely: Eω0(〈h,Yt〉) = 〈ω,h〉, for any test function h, where ω = rot u, u denotes the velocity solution of Navier-Stokes equation. The support of the random measure Yt increases or decreases in one unit when the underlying process hits ∂Ω; this stochastic phenomenon corresponds to the creation-annihilation of vortex...
B-spline collocation methods for numerical solutions of the Burgers' equation.
Bubble-enriched least-squares finite element method for transient advective transport.
Calculation of low Mach number acoustics : a comparison of MPV, EIF and linearized Euler equations
The calculation of sound generation and propagation in low Mach number flows requires serious reflections on the characteristics of the underlying equations. Although the compressible Euler/Navier-Stokes equations cover all effects, an approximation via standard compressible solvers does not have the ability to represent acoustic waves correctly. Therefore, different methods have been developed to deal with the problem. In this paper, three of them are considered and compared to each other. They...
Calculation of low Mach number acoustics: a comparison of MPV, EIF and linearized Euler equations
The calculation of sound generation and propagation in low Mach number flows requires serious reflections on the characteristics of the underlying equations. Although the compressible Euler/Navier-Stokes equations cover all effects, an approximation via standard compressible solvers does not have the ability to represent acoustic waves correctly. Therefore, different methods have been developed to deal with the problem. In this paper, three of them are considered and compared to each other....
Calculation of minimum critical Reynolds number for laminar-turbulent transition in pipe flows.
Calculation of the critical Stokes number for wide-stream impaction of potential flow over symmetric arc-nosed collectors.
Capillary surfaces in non-cylindrical domains.
Caractérisation variationnelle globale des flots canoniques et de contact dans leurs groupes de difféomorphismes
Cascade of phases in turbulent flows
This article is devoted to incompressible Euler equations (or to Navier-Stokes equations in the vanishing viscosity limit). It describes the propagation of quasi-singularities. The underlying phenomena are consistent with the notion of a cascade of energy.
Cauchy problem for the non-newtonian viscous incompressible fluid
We study the Cauchy problem for the non-Newtonian incompressible fluid with the viscous part of the stress tensor , where the nonlinear function satisfies or . First, the model for the bipolar fluid is studied and existence, uniqueness and regularity of the weak solution is proved for for both models. Then, under vanishing higher viscosity , the Cauchy problem for the monopolar fluid is considered. For the first model the existence of the weak solution is proved for , its uniqueness and...
Caustic consideration of long planetary wave packet analysis in the continuously stratified ocean.
Cell centered Galerkin methods for diffusive problems
In this work we introduce a new class of lowest order methods for diffusive problems on general meshes with only one unknown per element. The underlying idea is to construct an incomplete piecewise affine polynomial space with optimal approximation properties starting from values at cell centers. To do so we borrow ideas from multi-point finite volume methods, although we use them in a rather different context. The incomplete polynomial space replaces classical complete polynomial spaces in discrete...
Cell centered Galerkin methods for diffusive problems
In this work we introduce a new class of lowest order methods for diffusive problems on general meshes with only one unknown per element. The underlying idea is to construct an incomplete piecewise affine polynomial space with optimal approximation properties starting from values at cell centers. To do so we borrow ideas from multi-point finite volume methods, although we use them in a rather different context. The incomplete polynomial space replaces classical complete polynomial spaces...
Central-upwind schemes for the Saint-Venant system
We present one- and two-dimensional central-upwind schemes for approximating solutions of the Saint-Venant system with source terms due to bottom topography. The Saint-Venant system has steady-state solutions in which nonzero flux gradients are exactly balanced by the source terms. It is a challenging problem to preserve this delicate balance with numerical schemes. Small perturbations of these states are also very difficult to compute. Our approach is based on extending semi-discrete central schemes...
Central-Upwind Schemes for the Saint-Venant System
We present one- and two-dimensional central-upwind schemes for approximating solutions of the Saint-Venant system with source terms due to bottom topography. The Saint-Venant system has steady-state solutions in which nonzero flux gradients are exactly balanced by the source terms. It is a challenging problem to preserve this delicate balance with numerical schemes. Small perturbations of these states are also very difficult to compute. Our approach is based on extending semi-discrete central...
Certain rélations existant entre les dérivées partielles des deux côtés de l'onde de choc