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 [29] applied Glimm's method to the numerical solution of homogeneous
hyperbolic conservation laws. Colella [31] 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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Numerical Hydrodynamics in Special Relativity
Jose Maria Martí and Ewald Müller http://www.livingreviews.org/lrr-1999-3 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |