NeuralFVM: Neural-physics-based Finite Volume Method for Turbulent Flows Using the $k$-$\omega$ Model

TL;DR

NeuralFVM introduces a GPU-accelerated neural-physics solver based on finite volume methods and the $k$-$omega$ turbulence model, enabling efficient, accurate simulations of turbulent flows with deep learning integration.

Contribution

This work develops NeuralFVM, a novel neural-physics solver that reformulates FVM equations as local tensor operations, incorporating an operator-splitting strategy for stiff turbulence terms and a neural multigrid for pressure-velocity coupling.

Findings

Achieves 19-46x speedup over CPU implementations.

Demonstrates close agreement with ANSYS Fluent in various flow scenarios.

Provides a framework compatible with machine learning workflows for turbulence modeling.

Abstract

In this work, we develop a neural-physics solver based on finite volume method (FVM), namely NeuralFVM, for turbulent flows by implementing the standard $k$-$\omega$ model designed for efficient Graphics Processing Unit (GPU) execution. The governing equations for fluid flow and heat transfer are reformulated as local tensor operations using convolution-based stencil operators, which enables compatibility with deep learning libraries while preserving the conservative properties of the FVM. A key challenge in implementing the turbulent model within such a framework is the treatment of the stiff destruction terms in the $k$ and $\omega$ transport equations. To address this issue, an operator-splitting strategy is introduced in which the stiff destruction terms are handled semi-implicitly while the remaining terms are advanced explicitly. This formulation avoids global matrix assembly and allows the entire solver to be implemented using local tensor operations. In addition, the pressure-velocity coupling is solved using a convolution-based geometric multigrid algorithm embedded within a neural network architecture. The resulting NeuralFVM solver is validated through comparison with simulations conducted using the commercial CFD software ANSYS Fluent for several channel-flow configurations and an indoor airflow scenario. The results demonstrate close agreement in velocity, temperature, and turbulence quantities, confirming the accuracy of the proposed approach. The developed GPU framework achieves a speedup of around 19-46 times compared with its Central Processing Unit (CPU) counterpart under different meshes. Moreover, the proposed solver naturally integrates with machine learning workflows, providing a promising foundation for future data-driven turbulence modeling and optimization.