A turbulence reduced order model based on non-interpolated convolutional autoencoder

基于非插值卷积自编码器的湍流降阶模型

¹ School of Computer Engineering and Science, Shanghai University, Shanghai 200444, China
² Institute of Artificial Intelligence, Shanghai University, Shanghai 200444, China
³ Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China

Received: 7 December 2023

Abstract

Reduced-order modeling stands as a pivotal method in curbing the computational expenses linked with expansive fluid dynamics quandaries by employing proxy numerical simulations. Within this realm, downscaling and reconstruction methods serve as fundamental constituents of reduced-order modeling. The traditional intrinsic orthogonal decomposition relies on linear mapping, often relinquishing a substantial amount of nonlinear flow information within the flow field. Meanwhile, autoencoders equipped with fully-connected structures, maybe encounter a parameter explosion when handling larger-scale flow field meshes, impeding effective training. Convolutional autoencoders necessitate uniform interpolation across the flow field to attain a uniform flow field snapshot, yet this process frequently introduces interpolation errors and unwarranted temporal overheads. This paper introduces an innovative solution: a non-interpolated convolutional autoencoder, designed to extract nonlinear features from the flow field while curbing parameter count, evading interpolation errors, and mitigating additional computational burdens. Illustratively, in a two-dimensional cylindrical winding flow scenario, both the reduced dimensional reconstruction display root mean square errors of approximately 1×10^-3. Notably, the velocity cloud and absolute error cloud vividly exhibit the non-interpolated convolutional autoencoder's remarkable prowess in reconstruction.

摘要

降阶模型通过代理数值模拟, 有效降低了大规模流体动力学问题的计算成本。其中, 降维和重构方法是降阶模型的关键组成部分。传统的本征正交分解基于线性映射, 常常在处理流场时损失大量非线性流动信息。全连接结构的自编码器在处理较大规模流场网格时会导致模型参数爆炸, 难以有效训练。为了获得均匀流场快照, 卷积自编码器一般需要在流场上进行均匀插值, 这通常伴随着插值误差和不必要的时间成本。为解决这些问题, 提出了一种创新的非插值卷积自编码器, 该模型可以提取流场的非线性特征, 降低参数量, 避免插值误差和额外的计算成本。在二维圆柱绕流算例上, 降维重构的均方根误差均约为1×10^-3, 速度云图和绝对误差云图展示了非插值卷积自编码器在重构方面的卓越性能。