Reducing spatial discretization error on coarse CFD simulations using an openFOAM-embedded deep learning framework

IF 8.7 2区 工程技术 Q1 Mathematics
J. Gonzalez-Sieiro, D. Pardo, V. Nava, V. M. Calo, M. Towara
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Abstract

We propose a method for reducing the spatial discretization error of coarse computational fluid dynamics (CFD) problems by enhancing the quality of low-resolution simulations using deep learning. We feed the model with fine-grid data after projecting it to the coarse-grid discretization. We substitute the default differencing scheme for the convection term by a feed-forward neural network that interpolates velocities from cell centers to face values to produce velocities that approximate the down-sampled fine-grid data well. The deep learning framework incorporates the open-source CFD code OpenFOAM, resulting in an end-to-end differentiable model. We automatically differentiate the CFD physics using a discrete adjoint code version. We present a fast communication method between TensorFlow (Python) and OpenFOAM (c++) that accelerates the training process. We applied the model to the flow past a square cylinder problem, reducing the error from 120% to 25% in the velocity for simulations inside the training distribution compared to the traditional solver using an x8 coarser mesh. For simulations outside the training distribution, the error reduction in the velocities was about 50%. The training is affordable in terms of time and data samples since the architecture exploits the local features of the physics.

Abstract Image

使用嵌入深度学习框架的 openFOAM 减少粗糙 CFD 模拟的空间离散化误差
我们提出了一种利用深度学习提高低分辨率模拟质量,从而减少粗计算流体动力学(CFD)问题空间离散化误差的方法。我们在对模型进行粗网格离散化投影后,向其输入细网格数据。我们用一个前馈神经网络替代了对流项的默认差分方案,该网络将速度从单元中心插值到面值,从而产生与向下采样的细网格数据近似的速度。深度学习框架结合了开源 CFD 代码 OpenFOAM,形成了端到端的可微分模型。我们使用离散邻接代码版本自动微分 CFD 物理。我们提出了一种 TensorFlow(Python)和 OpenFOAM(c++)之间的快速通信方法,可加速训练过程。我们将该模型应用于流过方形圆柱体的问题,与使用 x8 粗网格的传统求解器相比,在训练分布内模拟的速度误差从 120% 降至 25%。对于训练分布以外的模拟,速度误差减少了约 50%。由于该结构利用了物理学的局部特征,因此在时间和数据样本方面都可以负担得起训练费用。
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来源期刊
Engineering with Computers
Engineering with Computers 工程技术-工程:机械
CiteScore
16.50
自引率
2.30%
发文量
203
审稿时长
9 months
期刊介绍: Engineering with Computers is an international journal dedicated to simulation-based engineering. It features original papers and comprehensive reviews on technologies supporting simulation-based engineering, along with demonstrations of operational simulation-based engineering systems. The journal covers various technical areas such as adaptive simulation techniques, engineering databases, CAD geometry integration, mesh generation, parallel simulation methods, simulation frameworks, user interface technologies, and visualization techniques. It also encompasses a wide range of application areas where engineering technologies are applied, spanning from automotive industry applications to medical device design.
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