相关论文: Exact and numerical solutions of the Riemann probl…
This report addresses the solution of Riemann problems for hyperbolic equations when the nonlinear characteristic fields loose their genuine nonlinearity. In this context, exact solvers for nonconvex 1D Riemann problems are developed. First…
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…
In this article, we develop a new hyperbolic model governing the first-order dynamics of a thin film flow under the influence of gravity and solute transport. The obtained system turns out to be a non-symmetric Keyfitz-Kranzer type system.…
The shear shallow water model is a higher order model for shallow flows which includes some shear effects that are neglected in the classical shallow models. The model is a non-conservative hyperbolic system which can admit shocks,…
In this paper, we present a unified nonequilibrium model of continuum mechanics for compressible multiphase flows. The model, which is formulated within the framework of Symmetric Hyperbolic Thermodynamically Compatible (SHTC) equations,…
A new Riemann solver is built to address numerical resolution of complex flow models. The research direction is closely linked to a variant of the Baer and Nunziato (1986) model developed in Saurel et al. (2017a). This recent model provides…
For nonlinear hyperbolic systems of conservation laws in one space variable, we establish the existence of nonclassical entropy solutions exhibiting nonlinear interactions between shock waves with strong strength. The proposed theory is…
We construct the solution of the Riemann problem for the shallow water equations with discontinuous topography. The system under consideration is non-strictly hyperbolic and does not admit a fully conservative form, and we establish the…
A recently introduced two-phase flow model by Chun Shen is studied in this work. The model is derived to describe the dynamics of immersed water bubbles in liquid water as carrier. Several assumptions are made to obtain a reduced form of…
The Riemann problem is one of the basic building blocks for numerical methods in computational fluid mechanics. Nonetheless, there are still open questions and gaps in theory and modelling for situations with complex thermodynamic behavior.…
This paper introduces a novel wave front tracking framework for reconstructing unknown flux functions in $2\times 2$ hyperbolic conservation laws, extending beyond the well-studied scalar case. By analyzing Riemann solutions at fixed…
A system of hyperbolic conservation laws $$ \partial_t u + \partial_x \partial_u Q = 0, \quad Q = u_1^3 / 3 + u_1 u_2^2, \qquad u = u(x,t) \in\mR^2, $$ as well as its viscous regularization $$ \partial_t u + \partial_x \partial_u Q = \calM…
In previous work, we developed a topological framework for solving Riemann initial-value problems for a system of conservation laws. Its core is a differentiable manifold, called the wave manifold, with points representing shock and…
By the flux-approximation method, we study limits of Riemann solutions to the Brio system with two independent parameters. The Riemann problem of the perturbed system is solved analytically, and four kinds of solutions are obtained…
Derivation of governing equations for multiphase flow on the base of thermodynamically compatible systems theory is presented. The mixture is considered as a continuum in which the multiphase character of the flow is taken into account. The…
Recently the barotropic two fluid model belonging to the class of \emph{symmetric hyperbolic thermodynamically compatible} (SHTC) systems was studied in detail in \cite{Thein2022}. There the question was raised whether the dissipative…
We review recent interest in the relativistic Riemann problem as a method for generating a non-equilibrium steady state. In the version of the problem under con- sideration, the initial conditions consist of a planar interface between two…
A solution of a Riemann problem for a strictly hyperbolic system of conservation laws is traditionally expected to consist of rarefaction waves, jump discontinuities, and constant states. In this paper, we investigate whether a Riemann…
A solution of the Riemann problem is constructed for a nonstrictly hyperbolic inhomogeneous system of equations describing one-dimensional cold plasma oscillations. Each oscillation period includes one rarefaction wave and one shock wave…
We consider a system of two conservation laws and provide a detailed description of both classical and non-classical self-similar Riemann solutions. In particular, we demonstrate the existence of overcompressive delta shocks as singular…