论文标题
混沌电交流的稀疏非线性模型
Sparse nonlinear models of chaotic electroconvection
论文作者
论文摘要
对流是一种基本的流体转运现象,其中流体的大规模运动是由热梯度或电势驱动的。建模对流引起了混乱理论的发展和多物理系统的减少阶层建模。但是,这些模型仅限于相对简单的热对流现象。在这项工作中,我们开发了一个在高电动雷利数字上进行混沌电交换的降级模型。该系统中的混乱与从瑞利 - 贝纳德对流获得的标准Lorenz模型有关,尽管我们的系统是由流体,电荷密度和电场之间更复杂的三向耦合驱动的。相干结构是通过适当的正交分解(POD)从时间和空间分辨的电荷密度场中提取的。然后,使用非线性动力学(Sindy)算法的稀疏识别来为这些相干结构的混乱时间演变而开发非线性模型,该算法被限制为保留原始系统中观察到的对称性。所得模型表现出原始高维系统的主要混沌动力学,并与简单的还原阶模型捕获了必需的非线性相互作用。
Convection is a fundamental fluid transport phenomenon, where the large-scale motion of a fluid is driven, for example, by a thermal gradient or an electric potential. Modeling convection has given rise to the development of chaos theory and the reduced-order modeling of multiphysics systems; however, these models have been limited to relatively simple thermal convection phenomena. In this work, we develop a reduced-order model for chaotic electroconvection at high electric Rayleigh number. The chaos in this system is related to the standard Lorenz model obtained from Rayleigh-Benard convection, although our system is driven by a more complex three-way coupling between the fluid, the charge density, and the electric field. Coherent structures are extracted from temporally and spatially resolved charge density fields via proper orthogonal decomposition (POD). A nonlinear model is then developed for the chaotic time evolution of these coherent structures using the sparse identification of nonlinear dynamics (SINDy) algorithm, constrained to preserve the symmetries observed in the original system. The resulting model exhibits the dominant chaotic dynamics of the original high-dimensional system, capturing the essential nonlinear interactions with a simple reduced-order model.