High resolution methods for the Buckley-Leverett equation.
High resolution schemes for hyperbolic conservation laws
History-dependent scalar conservation laws
Hölder-continuous solution for a nonlinear elasticity system.
How parabolic free boundaries approximate hyperbolic fronts.
Hybrid central-upwind schemes for numerical resolution of two-phase flows
In this paper we present a methodology for constructing accurate and efficient hybrid central-upwind (HCU) type schemes for the numerical resolution of a two-fluid model commonly used by the nuclear and petroleum industry. Particularly, we propose a method which does not make use of any information about the eigenstructure of the jacobian matrix of the model. The two-fluid model possesses a highly nonlinear pressure law. From the mass conservation equations we develop an evolution equation which...
Hybrid central-upwind schemes for numerical resolution of two-phase flows
In this paper we present a methodology for constructing accurate and efficient hybrid central-upwind (HCU) type schemes for the numerical resolution of a two-fluid model commonly used by the nuclear and petroleum industry. Particularly, we propose a method which does not make use of any information about the eigenstructure of the Jacobian matrix of the model. The two-fluid model possesses a highly nonlinear pressure law. From the mass conservation equations we develop an evolution equation which...
Hydrodynamic limit for perturbation of a hyperbolic equilibrium point in two-component systems
Hyperbolic systems of conservation laws.
This is a survey paper, written in the occasion of an invited talk given by the author at the Universidad Complutense in Madrid, October 1998. Its purpose is to provide an account of some recent advances in the mathematical theory of hyperbolic systems of conservation laws in one space dimension. After a brief review of basic concepts, we describe in detail the method of wave-front tracking approximation and present some of the latest results on uniqueness and stability of entropy weak solutions....
Hyperbolické systémy, entropie a metoda konečných objemů
Ill-posedness of the Cauchy problem for totally degenerate system of conservation laws.
Infinitely narrow soliton solutions to systems of conservation laws.
Initial boundary value problem for a system in elastodynamics with viscosity.
Intégrabilité d'une classe de systèmes de lois de conservation.
Integrable anisotropic evolution equations on a sphere.
Interaction de chocs
Interface model coupling via prescribed local flux balance
This paper deals with the non-conservative coupling of two one-dimensional barotropic Euler systems at an interface at x = 0. The closure pressure laws differ in the domains x < 0 and x > 0, and a Dirac source term concentrated at x = 0 models singular pressure losses. We propose two numerical methods. The first one relies on ghost state reconstructions at the interface while the second is based on a suitable relaxation framework. Both methods satisfy a well-balanced property for stationary...
Interface tracking method for compressible multifluids
This paper is concerned with numerical methods for compressible multicomponent fluids. The fluid components are assumed immiscible, and are separated by material interfaces, each endowed with its own equation of state (EOS). Cell averages of computational cells that are occupied by several fluid components require a “mixed-cell” EOS, which may not always be physically meaningful, and often leads to spurious oscillations. We present a new interface tracking algorithm, which avoids using mixed-cell...
Invariant tensors and partial differential equations.
Justification de l'optique géométrique non linéaire pour un système de lois de conservation