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Statistical solutions are time-parameterized probability measures on spacesof integrable functions, that have been proposed recently as a framework forglobal solutions and uncertainty quantification for multi-dimensionalhyperbolic system of conservation laws. By combining high-resolution finitevolume methods with a Monte Carlo sampling procedure, we present a numericalalgorithm to approximate statistical solutions. Under verifiable assumptions onthe finite volume method, we prove that the approximations, generated by theproposed algorithm, converge in an appropriate topology to a statisticalsolution. Numerical experiments illustrating the convergence theory andrevealing interesting properties of statistical solutions, are also presented.

Statistical solutions of hyperbolic systems of conservation laws: numerical approximation