Advanced Methods in Relativistic Hydrodynamics



Simulation produced by the "Cactus3-Code", AEI, AUTH, SISSA, UVEG, WashU

The solution of the Riemann problem attracted a wider interest when it was realized that its numerical solution could be implemented as building blocks in the construction of numerical Godunov-type methods for the accurate solution of the hydrodynamical equations. In such methods, the computational domain is discretized and each interface between two adjacent grid-zones is used to construct the initial left and right states of a ``local'' Riemann problem. The evolution of the hydrodynamical equations is then obtained through the solution of the sequence of local Riemann problems set up at the interfaces between successive grid-zones. High Resolution Shock Capturing (HRSC) are among the most used applications of Godunov methods and have allowed numerical simulations of unprecedented accuracy also in fully relativistic 3D applications. The group in SISSA is constantly looking at approaches in relativistic hydrodynamics that can improve either the accuracy or the efficiency in the solution of the hydrodynamical equations.

  • Efficient Riemann Solvers: a new approach to the solution of the exact Riemann problem in 1D which optimises both computational costs and simplicity of implementation has been investigated in SISSA.  This new method can also be extended to the case of nonzero tangential velocities and can therefore be implemented also in multi-dimensional relativistic hydrodynamics codes. More information can be found in these papers:I and II

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  • New Relativistic effects: new effects have been found in the evolution of the 3D relativistic Riemann problem. By varying the initial tangential velocities (while otherwise maintaining the initial states unmodified) a shock front can be transformed into a rarefaction wave and viceversa. More information can be found in this paper

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    The movie on the left is an example of these new relativistic effects in which a wave pattern consisting of one shock and one rarefaction wave is transformed into a wave pattern consisting in two rarefaction waves as the tangential velocity on one side of the initial discontinuity is increased (this is indicated with the number appearing in the upper left corner)
    The movie on the right is another  example of these new relativistic effects in which a wave pattern consisting of one shock and one rarefaction wave is transformed into a wave pattern consisting in two shocks as the tangential velocity on one side of the initial discontinuity is increased (this is indicated with the number appearing in the upper left corner).

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    Page created by: Luciano Rezzolla
    Last change made: Tue Apr 20 12:56:06 CEST 2004