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We present a five-wave Riemann solver for the equations of ideal relativistic magnetohydrodynamics. Our solver can be regarded as a relativistic extension of the five-wave HLLD Riemann solver initially developed by Miyoshi and Kusano for…

Astrophysics · Physics 2015-05-13 A. Mignone , M. Ugliano , G. Bodo

We present an analytic solution of the Riemann problem for the equations of relativistic hydrodynamics with the ultra-relativistic equation of state and non-zero tangential velocities. A 3-dimensional numerical code solving such equations…

Mathematical Physics · Physics 2010-07-12 Patryk Mach

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…

Analysis of PDEs · Mathematics 2026-05-22 Bradley J. Plohr , Stephen Schecter , Dan Marchesin

We present a general and practical procedure to solve the general relativistic hydrodynamic equations by using any of the special relativistic Riemann solvers recently developed for describing the evolution of special relativistic flows.…

Astrophysics · Physics 2007-05-23 Jose A. Pons , Jose A. Font , Jose M. Ibanez , Jose M. Marti , Juan A. Miralles

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…

High Energy Physics - Theory · Physics 2016-11-23 Michael Spillane , Christopher P. Herzog

The Generalized Riemann Problems (GRP) for nonlinear hyperbolic systems of balance laws in one space dimension are now well-known and can be formulated as follows: Given initial-data which are smooth on two sides of a discontinuity,…

Numerical Analysis · Mathematics 2013-03-13 Jianzhen Qian , Jiequan Li , Shuanghu Wang

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…

Analysis of PDEs · Mathematics 2023-03-28 Olga S. Rozanova

This paper proposes a second-order accurate direct Eulerian generalized Riemann problem (GRP) scheme for the ten-moment Gaussian closure equations with source terms. The generalized Riemann invariants associated with the rarefaction waves,…

Numerical Analysis · Mathematics 2024-07-08 Jiangfu Wang , Huazhong Tang

Our contribution concerns with the numerical solution of the 3D general relativistic hydrodynamical system of equations within the framework of the 3+1 formalism. We summarize the theoretical ingredients which are necessary in order to…

Astrophysics · Physics 2007-05-23 J. M. Ibanez , M. A. Aloy , J. A. Font , J. M. Marti , J. A. Miralles , J. A. Pons

We present an extension of the Piecewise Parabolic Method to special relativistic fluid dynamics in multidimensions. The scheme is conservative, dimensionally unsplit, and suitable for a general equation of state. Temporal evolution is…

Astrophysics · Physics 2009-11-11 A. Mignone , T. Plewa , G. Bodo

We construct a large family of exact solutions to the hyperbolic system of 3 equations of ideal granular hydrodynamics in several dimensions for arbitrary adiabatic index $\gamma$. In dependence of initial conditions these solutions can…

Mathematical Physics · Physics 2013-02-07 Olga S Rozanova

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…

Numerical Analysis · Mathematics 2022-03-14 Changsheng Yu , Tiegang Liu , Chengliang Feng

We investigate the Riemann problem for the shallow water equations with variable and (possibly) discontinuous topography and provide a complete description of the properties of its solutions: existence; uniqueness in the non-resonant…

Analysis of PDEs · Mathematics 2015-05-28 Philippe G. LeFloch , Mai Duc Thanh

Under the hypothesis of small deformations, the equations of 1D elastodynamics write as a 2 x 2 hyperbolic system of conservation laws. Here, we study the Riemann problem for convex and nonconvex constitutive laws. In the convex case, the…

Classical Physics · Physics 2022-02-08 H Berjamin , B Lombard , G Chiavassa , N Favrie

We have built a code to numerically solve the Riemann problem in ideal magnetohydrodynamics (MHD) for an arbitrary initial condition to investigate a variety of solutions more thoroughly. The code can handle not only regular solutions, in…

High Energy Astrophysical Phenomena · Physics 2015-06-11 Kazuya Takahashi , Shoichi Yamada

We utilize a three-dimensional manifold to solve Riemann Problems that arise from a system of two conservation laws with quadratic flux functions. Points in this manifold represent potential shock waves, hence its name wave manifold. This…

In this paper, we describe certain crucial steps in the development of an algorithm for finding the Riemann solution in systems of conservation laws. We relax the classical hypotheses of strict hyperbolicity and genuine nonlinearity of Lax.…

Analysis of PDEs · Mathematics 2019-02-13 A. C. Alvarez , G. T. Goedert , D. Marchesin

Redatuming is a data processing technique to transform measurements recorded in one acquisition geometry to an analogous data set corresponding to another acquisition geometry, for which there are no recorded measurements. We consider a…

Analysis of PDEs · Mathematics 2017-10-10 Maarten V. de Hoop , Paul Kepley , Lauri Oksanen

We consider the problem of resolving all pairwise interactions of shock waves, contact waves, and rarefaction waves in 1-dimensional flow of an ideal polytropic gas. Resolving an interaction means here to determine the types of the three…

Analysis of PDEs · Mathematics 2015-05-28 Geng Chen , Erik E. Endres , Helge Kristian Jenssen

Fluid dynamic limit to compressible Euler equations from compressible Navier-Stokes equations and Boltzmann equation has been an active topic with limited success so far. In this paper, we consider the case when the solution of the Euler…

Analysis of PDEs · Mathematics 2010-11-10 Feimin Huang , Yi Wang , Tong Yang