Table 1:
Solution of the relativistic Riemann problem at t = 0.4 with initial data = 10 ^{3},
= 1.0, = 0.0, = 10^{–2}, = 1.0, and = 0.0 for 9 different combinations
of tangential velocities in the left () and right () initial state. An ideal EOS with = 5/3
was assumed. The various quantities in the table are: the density in the intermediate state left ()
and right () of the contact discontinuity, the pressure in the intermediate state (), the flow
speed in the intermediate state (), the speed of the shock wave (), and the velocities of the
head () and tail () of the rarefaction wave. |

Table 2:
Pressure , velocity , and densities (left), (right) for the intermediate state obtained for the two-shock approximation of Balsara (B) [13] and of Dai and Woodward (DW) [64] compared to the exact solution (Exact) for the Riemann problems defined in Section 6.2. |

Table 3:
High-resolution shock-capturing methods using characteristic information. All the codes rely on a conservation form of the RHD equations with the exception of [295]. |

Table 4:
High-resolution shock-capturing methods avoiding the use of characteristic information. |

Table 5:
Code characteristics. |

Table 6:
Summary of relativistic shock heating test calculations by various authors in planar ( = 0), cylindrical ( = 1), and spherical ( = 2) geometry. W _{max} and are the
maximum inflow Lorentz factor and compression ratio error extracted from tables and figures of
the corresponding reference. W_{max} should only be considered as indicative of the maximum Lorentz
factor achievable by the respective method. Methods are described in Sections 3 and 4, and their
basic properties are summarized in Section 5 (Tables 3, 4, and 5). |

Table 7:
Initial data (pressure , density , velocity ) for two common relativistic blast wave test problems. The decay of the initial discontinuity leads to a shock wave (velocity , compression ratio ) and the formation of a dense shell (velocity , time-dependent width ) both propagating to the right. The gas is assumed to be ideal with an adiabatic index = 5/3. |

Table 8:
Summary of references where the blast wave problem 1 (defined in Table 7) has been considered in 1D, 2D and, 3D, respectively. Methods are described in Sections 3 and 4, and their basic properties are summarized in Section 5 (Tables 3, 4, and 5). Note that CD stands for contact discontinuity. |

Table 9:
Summary of references where the blast wave Problem 1 (defined in Table 7) has been considered in 1D, 2D, and 3D, respectively. Methods are described in Sections 3 and 4, and their basic properties are summarized in Section 5 (Tables 3, 4, and 5). Note that CD stands for contact discontinuity. |

Table 10:
Summary of references where the blast wave problem 2 (defined in Table 7) has been considered. Shock compression ratios are evaluated for runs with 400 numerical zones and at t 0.40, unless otherwise established. Methods are described in Sections 3 and 4, and their basic properties are summarized in Section 5 (Tables 3, 4, and 5). |

Table 11:
Initial data (pressure , density , velocity ) for the two relativistic blast wave collision test problem. The decay of the initial discontinuities (at x = 0.1 and x = 0.9) produces two shock waves (velocitis , compression ratios ) moving in opposite directions followed by two trailing dense shells (velocities , time-dependent widths ). The gas is assumed to be ideal with an adiabatic index = 1.4. |

Table 12:
Evaluation of numerical methods for SRHD. Methods have been categorized for clarity. |

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