A novel structure-preserving numerical method to solve random hyperbolic systems of conservation laws is presented. The method uses a concept of generalized, measure-valued solutions to random conservation laws. This yields a linear partial differential equation with respect to the Young measure and allows to compute the approximation based on linear programming problems. We analyze structure-preserving properties of the derived numerical method and discuss its advantages and disadvantages. We numerically demonstrate the approach on the one-dimensional Burgers and isentropic Euler equations and compare with stochastic collocation. In addition, we introduce a discontinuous-flux test in which different entropies used in the linear-program objective select different weak entropy solutions, and we report the corresponding changes in the moments and supports of the Young measure.

翻译：本文提出了一种新颖的保结构数值方法，用于求解随机双曲守恒律系统。该方法基于随机守恒律的广义测度值解概念，导出了关于Young测度的线性偏微分方程，从而可通过线性规划问题构建近似解。我们分析了该数值方法的保结构特性，并讨论了其优缺点。通过一维Burgers方程和等熵Euler方程的数值实验，展示了该方法的应用，并与随机配置法进行了比较。此外，我们引入了一个间断通量测试案例，其中线性规划目标函数采用的不同熵条件会选取不同的弱熵解，并报告了Young测度的矩与支撑集的相应变化。