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
, 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 [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.