Riemann problem
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Global III-posedness of the isentropic system of gas dynamics Open
We consider the isentropic compressible Euler system in 2 space dimensions with pressure law p ($\rho$) = $\rho$$^2$ and we show the existence of classical Riemann data, i.e. pure jump discontinuities across a line, for which there are inf…
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Explicit Soliton Structure Formation for the Riemann Wave Equation and a Sensitive Demonstration Open
The motive of the study was to explore the nonlinear Riemann wave equation, which describes the tsunami and tidal waves in the sea and homogeneous and stationary media. This study establishes the framework for the analytical solutions to t…
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A high-performance integrated hydrodynamic modelling system for urban flood simulations Open
A new High-Performance Integrated hydrodynamic Modelling System (Hi-PIMS) is tested for urban flood simulation. The software solves the two-dimensional shallow water equations using a first-order accurate Godunov-type shock-capturing schem…
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The vanishing pressure limits of Riemann solutions to the Chaplygin gas equations with a source term Open
We study the vanishing pressure limits of Riemann solutions to the Chaplygin gas equations with a source term. The phenomena of concentration and cavitation to Chaplygin gas equations with a friction term are identified and analyzed as the…
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Pressure-based algorithm for compressible interfacial flows with acoustically-conservative interface discretisation Open
A pressure-based algorithm for the simulation of compressible interfacial flows is presented. The algorithm is based on a fully-coupled finite-volume framework for unstructured meshes with collocated variable arrangement, in which the gove…
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Experimental Generation of Riemann Waves in Optics: A Route to Shock Wave Control Open
We report the first observation of Riemann (simple) waves, which play a crucial role for understanding the dynamics of any shock-bearing system. This was achieved by properly tailoring the phase of an ultrashort light pulse injected into a…
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A simple well-balanced and positive numerical scheme for the shallow-water system Open
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SWE-SPHysics Simulation of Dam Break Flows at South-Gate Gorges Reservoir Open
This paper applied a Smoothed Particle Hydrodynamics (SPH) approach to solve Shallow Water Equations (SWEs) to study practical dam-break flows. The computational program is based on the open source code SWE-SPHysics, where a Monotone Upstr…
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Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic Open
We consider the follow-the-leader approximation of the Aw-Rascle-Zhang (ARZ) model for traffic flow in a multi population formulation. We prove rigorous convergence to weak solutions of the ARZ system in the many particle limit in presence…
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A 3D finite element ALE method using an approximate Riemann solution Open
Summary Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann‐like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite…
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Implementation of advanced Riemann solvers in a neutrino-radiation magnetohydrodynamics code in numerical relativity and its application to a binary neutron star merger Open
We implement advanced Riemann solvers HLLC and HLLD \cite{Mignone:2005ft,MUB:2009} together with an advanced constrained transport scheme \cite{Gardiner:2007nc} in a numerical-relativity neutrino-radiation magnetohydrodynamics code. We val…
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A constrained transport method for the solution of the resistive relativistic MHD equations Open
We describe a novel Godunov-type numerical method for solving the equations\nof resistive relativistic magnetohydrodynamics. In the proposed approach, the\nspatial components of both magnetic and electric fields are located at zone\ninterf…
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Riemann problems for a class of coupled hyperbolic systems of conservation laws with a source term Open
The Riemann problems for a class of coupled hyperbolic systems of conservation laws with a source term are studied. The Riemann solutions exactly include two kinds: delta-shock solutions and vacuum solutions. In order to see more clearly t…
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Macroscopic modeling of multilane motorways using a two-dimensional second-order model of traffic flow Open
Lane changing is one of the most common maneuvers on motorways. Although macroscopic traffic models are well known for their suitability to describe fast moving crowded traffic, most of these models are generally developed in a one-dimensi…
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Riemann problems and dispersive shocks in self-focusing media Open
The dynamical behavior resulting from an initial discontinuity in focusing\nmedia is investigated using a combination of numerical simulations and Whitham\nmodulation theory for the focusing nonlinear Schrodinger equation. Initial\nconditi…
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A new formulation for two-wave Riemann solver accurate at contact interfaces Open
This study proposes a new formulation for the Harten, Lax, and van Leer (HLL) type Riemann solver which is capable of solving contact discontinuities accurately but with robustness for strong shock. It is well known that the original HLL, …
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Conservative formulation for compressible multiphase flows Open
Derivation of governing equations for multiphase flow on the base of\nthermodynamically compatible systems theory is presented. The mixture is\nconsidered as a continuum in which the multiphase character of the flow is\ntaken into account.…
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Numerical simulation of water entry problems considering air effect using a multiphase Riemann-SPH model Open
The water entry is a classic fluid-structure interaction problem in ocean engineering. The prediction of impact loads on structure during the water entry is critical to some engineering applications. In this paper, a multiphase Riemann-SPH…
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Delta shocks and vacuum states in vanishing pressure limits of solutions to the relativistic Euler equations for generalized Chaplygin gas Open
The Riemann solutions for the relativistic Euler equations for generalized Chaplygin gas are considered.It is rigorously proved that, as the pressure vanishes, they tend to the two kinds of Riemann solutionsto the zero-pressure relativisti…
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Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations Open
We study the Riemann problem for multidimensional compressible isentropic Euler equations. Using the framework developed in Chiodaroli et al (2015 Commun. Pure Appl. Math. 68 1157-90), and based on the techniques of De Lellis and Szekelyhi…
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Is Discontinuous Reconstruction Really a Good Idea? Open
It has been almost automatically assumed for a quarter century that the numerical solution of hyperbolic conservation laws is best accomplished by making a reconstruction of the initial data that is only piecewise continuous. The effect of…
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Optical Random Riemann Waves in Integrable Turbulence Open
We examine integrable turbulence (IT) in the framework of the defocusing\ncubic one-dimensional nonlinear Schr\\"{o}dinger equation. This is done\ntheoretically and experimentally, by realizing an optical fiber experiment in\nwhich the def…
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Riemann problem for the photon fluid: Self-steepening effects Open
We consider the Riemann problem of evolution of initial discontinuities for\nthe photon fluid propagating in a normal dispersion fiber with account of\nself-steepening effects. The dynamics of light field is described by the\nnonlinear Sch…
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A low-dissipation HLLD approximate Riemann solver for a very wide range of Mach numbers Open
We propose a new Harten-Lax-van Leer discontinuities (HLLD) approximate Riemann solver to improve the stability of shocks and the accuracy of low-speed flows in multidimensional magnetohydrodynamic (MHD) simulations. Stringent benchmark te…
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A Riemann–Hilbert approach to the modified Camassa–Holm equation with nonzero boundary conditions Open
This paper aims at developing the Riemann–Hilbert problem approach to the modified Camassa–Holm (mCH) equation in the case when the solution is assumed to approach a non-zero constant at both infinities of the space variable. In this case,…
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Continuous Riemann solvers for traffic flow at a junction Open
The paper studies a class ofconservation law models for traffic flow on afamily of roads, near a junction. A Riemann Solver is constructed,where the incoming and outgoing fluxes depend Hölder continuouslyon the traffic density and on the d…
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Convergence of a Godunov scheme for conservation laws with a discontinuous flux lacking the crossing condition Open
We study a scalar conservation law whose flux has a single spatial discontinuity. There are many notions of (entropy) solution, the relevant concept being determined by the application. We focus on the so-called vanishing viscosity solutio…
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On the formation of Friedlander waves in a compressed-gas-driven shock tube Open
Compressed-gas-driven shock tubes have become popular as a laboratory-scale replacement for field blast tests. The well-known initial structure of the Riemann problem eventually evolves into a shock structure thought to resemble a Friedlan…
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An HLLC Riemann solver for resistive relativistic magnetohydrodynamics Open
We present a new approximate Riemann solver for the augmented system of\nequations of resistive relativistic magnetohydrodynamics (RRMHD) that belongs\nto the family of Harten-Lax-van Leer contact wave (HLLC) solvers. In HLLC\nsolvers, the…
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An Exact, Compressible One-Dimensional Riemann Solver for General, Convex Equations of State Open
This note describes an algorithm with which to compute numerical solutions to the one- dimensional, Cartesian Riemann problem for compressible flow with general, convex equations of state. While high-level descriptions of this approach are…