A direct Primitive Variable Recovery Scheme for hyperbolic conservative equations: The case of relativistic hydrodynamics

@article{AguayoOrtiz2018ADP,
  title={A direct Primitive Variable Recovery Scheme for hyperbolic conservative equations: The case of relativistic hydrodynamics},
  author={A Aguayo-Ortiz and Sebasti{\'a}n Mendoza and Daniel Olvera},
  journal={PLoS ONE},
  year={2018},
  volume={13}
}
In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the flux is applied in order avoid violation of both, the entropy and “Rankine-Hugoniot” jump conditions. The time evolution is then computed using a forward finite difference scheme… 

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References

SHOWING 1-10 OF 25 REFERENCES

Application of Central Upwind Scheme for Solving Special Relativistic Hydrodynamic Equations

A high-resolution shock-capturing central upwind scheme that uses the precise information of local propagation speeds to avoid the excessive numerical diffusion in the solution of the Einstein equations together with those of special relativistic hydrodynamics (SRHD).

An efficient shock-capturing central-type scheme for multidimensional relativistic flows. II. Magnetohydrodynamics

A third order shock-capturing numerical scheme for three-dimensional special relativistic magnetohydrodynamics (3-D RMHD) is presented and validated against several numerical tests. The simple and

THC: a new high-order finite-difference high-resolution shock-capturing code for special-relativistic hydrodynamics

We present THC: a new high-order flux-vector-splitting code for Newtonian and special-relativistic hydrodynamics designed for direct numerical simulations of turbulent flows. Our code implements a

Numerical Hydrodynamics in Special Relativity

This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a comprehensive review of

The Piecewise Parabolic Method (PPM) for Gas Dynamical Simulations

Exact solution of the 1D Riemann problem in Newtonian and relativistic hydrodynamics

The construction of the exact solution to the one dimensional Riemann problem is described and a detailed procedure of its implementation is described.

Multidimensional relativistic hydrodynamics: characteristics fields and modern high-resolution shock-capturing schemes

We have derived the spectral decomposition of the Jacobian matrices associated to the fluxes of the three-dimensional special relativistic hydrodynamics system of equations. The interest of this