Related papers: Solving Riemann Problems with a Topological Tool (…
In this paper we provide bound estimates for the two fastest wave speeds emerging from the solution of the Riemann problem for three well-known hyperbolic systems, namely the Euler equations of gas dynamics, the shallow water equations and…
This paper is concerned with the study of the main wave interactions in a system of conservation laws in geochemical modeling. We study the modeling of the chemical complexes on the rock surface. The presence of stable surface complexes…
Undercompressive shocks are a special type of discontinuities that satisfy the viscous profile criterion rather than the Lax inequalities. These shocks can appear as a solution to systems of two or more conservation laws. This paper…
We study the wave equation on a bounded domain of $\mathbb R^m$ and on a compact Riemannian manifold $M$ with boundary. We assume that the coefficients of the wave equation are unknown but that we are given the hyperbolic…
This paper is concerned with the Riemann problem of one-dimensional Euler equations with a singular source. The exact solution of this Riemann problem contains a stationary discontinuity induced by the singular source, which is different…
We introduce in this contribution the notion of partial Riemann problem. Recall that the Riemann problem describes a shock tube interaction between two given states ; the partial Riemann problem is a generalization of the previous concept…
This work presents the Riemann solution for three-phase flow in porous media under the condition that oil viscosity exceeds that of water and gas. We classify all Riemann solution problems for scenarios where the left states $L$ lie along…
We derive and establish a solution concept for the linear mountain wave problem in two dimensions. After linearizing the governing equations and a change of variables, the problem can be stated as a Dirichlet boundary value problem for a…
The standard analytical approach for studying gravity free-surface waves generated by a moving body often relies upon a linearization of the physical geometry, where the body is considered asymptotically small in one or several of its…
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 study the nonlinear dispersive waves including the rarefaction and dispersive shock waves in the discrete modified KdV equation through the numerical simulations of the dispersive Riemann problems. In particular, we…
We investigate the occurrence of topologically protected waves in classical fluids confined on curved surfaces. Using a combination of topological band theory and real space analysis, we demonstrate the existence of a system-independent…
Elastic wave propagation is a century-old problem. Unlike on a flat manifold, analytical solution is not well established for a curved manifold. In this study we take a step towards building an analytical framework for solving the elastic…
Gas injection in the context of the three-phase flow in porous media appears in applications such as Enhanced Oil Recovery, aquifer remediation, and carbon capture, utilization, and storage (CCUS). In general, this technique suffers from a…
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…
We investigate a model for traffic flow based on the Lighthill-Whitham-Richards model that consists of a hyperbolic conservation law with a discontinuous, piecewise-linear flux. A mollifier is used to smooth out the discontinuity in the…
We construct centered rarefaction wave solutions given background solutions to the compressible Euler equations. The flow considered in this article is the homentropic flow of perfect gas governed by compressible Euler equations and the…
We establish the hydrodynamic limit of the one-dimensional Boltzmann equation with hard-sphere collisions toward Riemann solutions of the compressible Euler system. The Riemann solutions covered by our result include generic superpositions…
The behaviour of the solutions to the Riemann problem for the isentropic Euler equations when the pressure vanishes is analysed. It is shown that any solution composed of a 1-shock wave and a 2-rarefaction wave tends to a two-shock wave…
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…