论文标题
数据驱动的替代建模方法，用于具有动态模式分解和歧管插值的时间依赖性不可压缩的Navier-Stokes方程
A Data-Driven Surrogate Modeling Approach for Time-Dependent Incompressible Navier-Stokes Equations with Dynamic Mode Decomposition and Manifold Interpolation
论文作者
论文摘要
这项工作引入了一种新型方法，用于减少时间依赖性参数部分微分方程的模型。使用由正交分解，动态模式分解和歧管插值组成的多步骤过程，提出的方法允许从几个大型模拟中准确恢复现场解决方案。 Rayleigh-Bénard腔问题的数值实验表明，在两个参数状态下，即〜中和高grashof数字，这种多步骤程序的有效性。后一种政权尤其具有挑战性，因为它接近湍流和混乱行为的开始。在时间周期解决方案背景下，该方法的主要优点是能够恢复采样数据中不存在的频率。
This work introduces a novel approach for data-driven model reduction of time-dependent parametric partial differential equations. Using a multi-step procedure consisting of proper orthogonal decomposition, dynamic mode decomposition and manifold interpolation, the proposed approach allows to accurately recover field solutions from a few large-scale simulations. Numerical experiments for the Rayleigh-Bénard cavity problem show the effectiveness of such multi-step procedure in two parametric regimes, i.e.~medium and high Grashof number. The latter regime is particularly challenging as it nears the onset of turbulent and chaotic behaviour. A major advantage of the proposed method in the context of time-periodic solutions is the ability to recover frequencies that are not present in the sampled data.
