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.,
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  applied Glimm’s method to the numerical solution of homogeneous hyperbolic conservation laws. Colella  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.
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