NeuralFVM: Neural-physics-based Finite Volume Method for Turbulent Flows Using the $k$-$ω$ Model
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| Main Authors: | , , , , , , , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917358001455104 |
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| author | Xue, Tingkai Jiao, Yu Ba, Te Wang, Jingliang Yang, Juntao See, Simon Chen, Boyang Heaney, Claire E. Pain, Christopher C. Kang, Chang Wei Mohamed, Mohamed Arif Bin Li, Hongying |
| author_facet | Xue, Tingkai Jiao, Yu Ba, Te Wang, Jingliang Yang, Juntao See, Simon Chen, Boyang Heaney, Claire E. Pain, Christopher C. Kang, Chang Wei Mohamed, Mohamed Arif Bin Li, Hongying |
| contents | In this work, we develop a neural-physics solver based on finite volume method (FVM), namely NeuralFVM, for turbulent flows by implementing the standard $k$-$ω$ 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 $ω$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_21869 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | NeuralFVM: Neural-physics-based Finite Volume Method for Turbulent Flows Using the $k$-$ω$ Model Xue, Tingkai Jiao, Yu Ba, Te Wang, Jingliang Yang, Juntao See, Simon Chen, Boyang Heaney, Claire E. Pain, Christopher C. Kang, Chang Wei Mohamed, Mohamed Arif Bin Li, Hongying Fluid Dynamics In this work, we develop a neural-physics solver based on finite volume method (FVM), namely NeuralFVM, for turbulent flows by implementing the standard $k$-$ω$ 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 $ω$ 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. |
| title | NeuralFVM: Neural-physics-based Finite Volume Method for Turbulent Flows Using the $k$-$ω$ Model |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2603.21869 |