Statistical solutions of hyperbolic systems of conservation laws: Numerical approximation
Statistical solutions of hyperbolic systems of conservation laws: Numerical approximation
复制标题
守恒定律双曲系统的统计解：数值近似
DOI：
10.1142/s0218202520500141
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发表时间：
2020
影响因子：
3.5
通讯作者：
Weber, F.
中科院分区：
文献类型：
--
作者：
Fjordholm, U. S.;Lye, K.;Mishra, S.;Weber, F.
统计解是可积函数空间上的时间参数化概率测度，最近被提出作为多维双曲守恒定律系统的全局解和不确定性量化的框架。通过将高分辨率有限体积方法与蒙特卡罗采样程序相结合，我们提出了一种近似统计解的数值算法。在有限体积方法的可验证假设下，我们证明了所提出的算法生成的近似值以适当的拓扑收敛到统计解。还提出了数值实验，说明了收敛理论并揭示了统计解的有趣特性。
Statistical solutions are time-parameterized probability measures on spaces of integrable functions, which have been proposed recently as a framework for global solutions and uncertainty quantification for multi-dimensional hyperbolic system of conservation laws. By combining high-resolution finite volume methods with a Monte Carlo sampling procedure, we present a numerical algorithm to approximate statistical solutions. Under verifiable assumptions on the finite volume method, we prove that the approximations, generated by the proposed algorithm, converge in an appropriate topology to a statistical solution. Numerical experiments illustrating the convergence theory and revealing interesting properties of statistical solutions are also presented.