论文标题
浅水方程的贪婪的非侵入性降低订单模型
A greedy non-intrusive reduced order model for shallow water equations
论文作者
论文摘要
在这项工作中，我们开发了非侵入性降低订单模型（NIROM），这些模型（NIROM）将正确的正交分解（POD）与径向基函数（RBF）插值方法相结合，以构建在大规模环境流动应用中产生的有效降低订单模型。通过评估代表河流流的测试问题的准确性和鲁棒性，将POD-RBF NIROM的性能与传统的非线性POD（NPOD）模型进行了比较。研究了不同的贪婪算法，以确定RBF近似的插值点的近乎理想的分布。提出了一种新的功率尺度残留贪婪（PSR刺激）算法，以解决现有贪婪方法的一些主要缺点。使用涉及沿海和河流动力学的二维浅水流量应用，通过数值实验研究了这些贪婪算法的相对性能。
In this work, we develop Non-Intrusive Reduced Order Models (NIROMs) that combine Proper Orthogonal Decomposition (POD) with a Radial Basis Function (RBF) interpolation method to construct efficient reduced order models for time-dependent problems arising in large scale environmental flow applications. The performance of the POD-RBF NIROM is compared with a traditional nonlinear POD (NPOD) model by evaluating the accuracy and robustness for test problems representative of riverine flows. Different greedy algorithms are studied in order to determine a near-optimal distribution of interpolation points for the RBF approximation. A new power-scaled residual greedy (psr-greedy) algorithm is proposed to address some of the primary drawbacks of the existing greedy approaches. The relative performances of these greedy algorithms are studied with numerical experiments using realistic two-dimensional (2D) shallow water flow applications involving coastal and riverine dynamics.
