The exact solution of the Riemann problem with non-zero tangential velocities in relativistic hydrodynamics

Abstract

We have generalised the exact solution of the Riemann problem in special relativistic hydrodynamics for arbitrary tangential flow velocities. The solution is obtained by solving the jump conditions across shocks plus an ordinary differential equation arising from the self-similarity condition along rarefaction waves, in a similar way as in purely normal flow. The dependence of the solution on the tangential velocities is analysed, and the impact of this result on the development of multidimensional relativistic hydrodynamic codes (of Godunov type) is discussed.

26 pages, 4 figures. Accepted for publication in Journal of Fluid Mechanics

Cited by in corpus (30)

• Three-dimensional relativistic simulations of rotating neutron-star collapse to a Kerr black hole
• Relativistic outflows from remnants of compact object mergers and their viability for short gamma-ray bursts
• Temporal and Angular Properties of GRB Jets Emerging from Massive Stars
• The Piecewise Parabolic Method for Multidimensional Relativistic Fluid Dynamics
• THC: a new high-order finite-difference high-resolution shock-capturing code for special-relativistic hydrodynamics
• WhiskyMHD: a new numerical code for general relativistic magnetohydrodynamics
• RAM: A Relativistic Adaptive Mesh Refinement Hydrodynamics Code
• Jet propagations, breakouts and photospheric emissions in collapsing massive progenitors of long duration gamma ray bursts
• 3D Simulations of Relativistic Precessing Jets Probing the Structure of Superluminal Sources
• Equation of State in Numerical Relativistic Hydrodynamics
• Relativistic Hydrodynamic Flows Using Spatial and Temporal Adaptive Structured Mesh Refinement
• Assessment of a high-resolution central scheme for the solution of the relativistic hydrodynamics equations
• Collimated Jet or Expanding Outflow: Possible Origins of GRBs and X-Ray Flashes
• AMRVAC and Relativistic Hydrodynamic simulations for GRB afterglow phases
• New Relativistic Effects in the Dynamics of Nonlinear Hydrodynamical Waves
• A Fast Numerical Scheme for Causal Relativistic Hydrodynamics with Dissipation
• Simulating gamma-ray binaries with a relativistic extension of RAMSES
• A New numerical scheme for resistive relativistic MHD using method of characteristics
• Protoneutron Star Convection Simulated with a New General Relativistic Boltzmann Neutrino Radiation-Hydrodynamics Code
• Exact solution of the hydrodynamical Riemann problem with nonzero tangential velocities and the ultrarelativistic equation of state
• A new scheme of causal viscous hydrodynamics for relativistic heavy-ion collisions: A Riemann solver for quark-gluon plasma
• Exact solution of one dimensional relativistic jet with relativistic equation of state
• A new relativistic hydrodynamics code for high-energy heavy-ion collisions
• A Multidimensional Relativistic Hydrodynamics Code with a General Equation of State
• Special Relativistic Hydrodynamics with CRONOS
• Glimm's Method for Relativistic Hydrodynamics
• A Simulation Study of Ultra-Relativistic Jets -- I. A New Code for Relativistic Hydrodynamics
• Effects of tangential velocity in the reactive relativistic Riemann problem
• Special Relativistic Smoothed Particle Hydrodynamics Based on Riemann Solver
• A new shock-capturing numerical scheme for ideal hydrodynamics