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arXiv · 2501.10104

Solving Random Hyperbolic Conservation Laws Using Linear Programming

Shaoshuai Chu·Michael Herty·Maria Lukacova-Medvidova·Yizhou Zhou
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Abstract

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.

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Shaoshuai Chu, Michael Herty, Maria Lukacova-Medvidova, Yizhou Zhou. 2025-01-17. Solving Random Hyperbolic Conservation Laws Using Linear Programming. https://arxiv.org/abs/2501.10104

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