Learning Divergence-Consistent Closure Models for Large-Eddy Simulation

Core Concepts

Proposing a new approach for learning divergence-consistent closure models for large-eddy simulation.

Abstract

The content introduces a novel neural network-based framework for large eddy simulation, focusing on discretization and filtering techniques. It discusses the importance of divergence-consistent filters and closure models for stable simulations. The article outlines the challenges in traditional closure models and presents a new approach to address model-data inconsistency. The study includes numerical experiments on turbulence in a periodic box to validate the proposed methods.

Stats

The Reynolds number Re = UL/ν is crucial for turbulent flow. Large eddy simulation (LES) aims to resolve large-scale features of flow. The commutator error term c(u, ¯u) is essential for closure models. The divergence-consistent face-averaging filter preserves the divergence-free constraint. Convolutional neural networks are commonly used for closure modeling.

Quotes

"We propose a new neural network based large eddy simulation framework." "Face-averaging filter preserves the divergence-free constraint for the filtered velocity."

Key Insights Distilled From

Discretize first, filter next

by Syve... at arxiv.org 03-28-2024

https://arxiv.org/pdf/2403.18088.pdf

Deeper Inquiries

How can the proposed divergence-consistent filter improve the accuracy of large-eddy simulations

The proposed divergence-consistent filter can improve the accuracy of large-eddy simulations by ensuring that the filtered velocity fields remain divergence-free. This is a crucial property in computational fluid dynamics as it helps maintain the physical integrity of the flow field. By preserving the divergence-free constraint during filtering, the filter reduces spurious numerical artifacts that can arise from non-conservative filtering methods. This leads to more accurate representations of the large-scale features of the flow, allowing for better predictions of turbulent behavior and flow dynamics. Additionally, the divergence-consistent filter helps in generating stable and reliable training data for neural closure models, which can further enhance the accuracy of the simulations.

What are the implications of using convolutional neural networks for closure modeling in computational fluid dynamics

Using convolutional neural networks (CNNs) for closure modeling in computational fluid dynamics offers several advantages. CNNs are well-suited for capturing complex patterns and relationships in structured data, making them effective for learning closure models from discretized flow data. In the context of computational fluid dynamics, CNNs can learn the mapping between the large-scale flow features and the closure terms, enabling the model to accurately predict the effects of unresolved scales on the resolved scales. This can lead to more accurate and stable simulations by providing a data-driven approach to modeling the sub-grid scale interactions. Additionally, CNNs can adapt to the non-linear and complex nature of fluid flow phenomena, allowing for more robust and efficient closure modeling compared to traditional approaches.

How does the study's approach to discretization and filtering differ from traditional methods in computational fluid dynamics

The study's approach to discretization and filtering differs from traditional methods in computational fluid dynamics by emphasizing a "discretize first, filter next" paradigm. This approach involves discretizing the partial differential equations (PDEs) first and then applying a discrete filter, as opposed to the traditional method of filtering the continuous equations and then discretizing. By discretizing first, the study ensures that the closure models are trained and applied in a consistent environment, leading to improved model-data consistency. Additionally, the introduction of a novel divergence-consistent discrete filter helps in preserving the divergence-free constraint in the filtered velocity fields, which is crucial for accurate large-eddy simulations. This approach addresses issues of stability and accuracy in closure modeling, offering a more robust framework for simulating turbulent flows.