Random choice solution of hyperbolic systems

Abstract A random choice method for solving nonlinear hyperbolic systems of conservation laws is presented. The method is rooted in Glimm's constructive proof that such systems have solutions. The solution is advanced in time by a sequence of operations which includes the solution of Riemann problems and a sampling procedure. The method can describe a complex pattern of shock wave and slip line interactions without introducing numerical viscosity and without a special handling of discontinuities. Examples are given of applications to one- and two-dimensional gas flow problems.