### 3.2 Relativistic Glimm’s method

Wen et al. [295] have extended Glimm’s random choice method [104] to 1D SRHD. They developed a
first-order accurate hydrodynamic code combining Glimm’s method (using an exact Riemann solver) with
standard finite difference schemes.
In the random choice method, given two adjacent states and at time , the value of the
numerical solution at time and position is given by the exact solution
of the Riemann problem evaluated at a randomly chosen point inside zone (j, j + 1), i.e.,

where is a random number in the interval [0, 1].
Besides being conservative on average, the main advantages of Glimm’s method are that it produces
both completely sharp shocks and contact discontinuities, and that it is free of diffusion and dispersion
errors.

Chorin [52] applied Glimm’s method to the numerical solution of homogeneous hyperbolic conservation
laws. Colella [57] proposed an accurate procedure of randomly sampling the solution of local Riemann
problems, and investigated the extension of Glimm’s method to two dimensions using operator splitting
methods.