Related papers: Coupled general Riemann problems for the Euler equ…
Numerical methods for the Euler equations with a singular source are discussed in this paper. The stationary discontinuity induced by the singular source and its coupling with the convection of fluid presents challenges to numerical…
We propose an approximate solver for multi-medium Riemann problems with materials described by a family of general Mie-Gr\"uneisen equations of state, which are widely used in practical applications. The solver provides the interface…
We discuss several approaches to generalized solutions of problems describing the motion of inviscid fluids. We propose a new concept of dissipative solution to the compressible Euler system based on a careful analysis of possible…
In this paper we present an approach to approximate numerically the solution of coupled hyperbolic conservation laws. The coupling is achieved through a fixed interface, in which interface conditions are linking the traces of both sides.…
We present a new formulation based on the classical Dirichlet-Neumann formulation for interface coupling problems in linearized elasticity. By using Taylor series expansions, we derive a new set of interface conditions that allow our…
We consider a sequence of approximate solutions to the compressible Euler system admitting uniform energy bounds and/or satisfying the relevant field equations modulo an error vanishing in the asymptotic limit. We show that such a sequence…
We investigate the relation between several generalized solution concepts for nonlinear PDE systems from fluid dynamics. More precisely, we study measure-valued solutions, dissipative weak solutions, and energy-variational solutions. For…
We study several $3\times 3$ systems of conservation laws, arising in modeling of two phase flow with rough porous media and traffic flow with rough road condition. These systems share several features. The systems are of mixed type, with…
This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical space is formulated in term of an augmented system of…
In this work we consider companion conservation laws to general systems of conservation laws. We investigate sufficient regularity for weak solutions to satisfy companion laws, assuming the fluxes to be $C^{1,\gamma}$, $0<\gamma<1$,…
Solutions to a class of conservation laws with discontinuous flux are constructed relying on the Crandall-Liggett theory of nonlinear contractive semigroups~\cite{CL}. In particular, the paper studies the existence of backward Euler…
The Riemann problem for first-order hyperbolic systems of partial differential equations is of fundamental importance for both theoretical and numerical purposes. Many approximate solvers have been developed for such systems; exact solution…
The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…
Entropy stabilization of the compressible Euler system is achieved by adapting the averages that are applied to the density and internal energy variables. The approach achieves non-linear robustness despite the use of simplified symmetric…
This paper is concerned with coupling conditions at junctions for transport models which differ in their fidelity to describe transient flow in gas pipelines. It also includes the integration of compressors between two pipes with possibly…
In this article, we study the gas expansion problem by turning a sharp corner into vacuum for the two-dimensional pseudo-steady compressible Euler equations with a convex equation of state. This problem can be considered as interaction of a…
We address the Riemann and Cauchy problems for systems of $n$ conservation laws in $m$ unknowns which are subject to $m-n$ constraints ($m\geq n$). Such constrained systems generalize systems of conservation laws in standard form to include…
A fully conservative sharp-interface method is developed for multiphase flows with phase change. The coupling between two phases is implemented via introducing the interfacial fluxes, which are obtained by solving a general Riemann problem…
We present a model of coupling between a point wise particle and a compressible inviscid fluid following the Euler equations. The interaction between the fluid and the particle is achieved through a drag force. It writes as the product of a…
The Cauchy problem for the linearization of a system of equations arising in the kinetic theory of a condensed gas of bosons near the critical temperature around one of its equilibria is solved for radially symmetric initial data. It is…