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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >A POD-based reduced-order model for free surface shallow water flows over real bathymetries for Monte-Carlo-type applications
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A POD-based reduced-order model for free surface shallow water flows over real bathymetries for Monte-Carlo-type applications

机译：基于POD的降阶模型，用于蒙特卡洛型应用的实际水深上的自由表面浅水流

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摘要

This paper presents a reduced-order model (ROM) to efficiently handle the uncertainties in the simulation of real free surface flows. The approach is dedicated to Monte-Carlo-type applications. The ROM is designed by projecting the non-linear shallow-water equations on a low-dimension basis, obtained using the proper orthogonal decomposition (POD) method. The non-linear terms are treated, through some specific approximations, to obtain the speedup expected from the reduced-order modeling methodology. The main motivation is the need for a faster numerical model to tackle the challenges posed by multiple-query applications such as optimal design or probabilistic analyses that use a large number of evaluations of the outputs for different values of input parameters. In the present work, the POD bases are constructed from data provided by a full-order finite volume model for a considered benchmark test with some given input parameters. This study first shows that the reduced-order model can simulate the dynamics of various dam break flows over variable bathymetries with significant speedups. A sensitivity analysis is then performed to evaluate to what extent the ROM can reproduce the dynamics of new scenarios obtained after varying the original input parameters. Good results are obtained for reasonable changes in the input parameters.
机译：本文提出了一种降阶模型（ROM），可以有效处理真实自由表面流模拟中的不确定性。该方法专用于蒙特卡洛类型的应用程序。通过使用适当的正交分解（POD）方法获得的低维非线性非线性浅水方程式投影来设计ROM。通过一些特定的近似处理非线性项，以获得从降阶建模方法中获得的加速效果。主要动机是需要一种更快的数值模型来应对多查询应用程序所带来的挑战，例如优化设计或概率分析，这些分析对输入参数的不同值使用大量的输出评估。在当前的工作中，POD库是由全阶有限体积模型提供的数据构建的，用于带有某些给定输入参数的基准测试。这项研究首先表明，降阶模型可以模拟具有明显加速比的可变水深上各种溃坝流的动力学。然后执行敏感性分析，以评估ROM可以在多大程度上重现在更改原始输入参数之后获得的新方案的动态。输入参数的合理更改可获得良好的结果。

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