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.