Finite difference physics-informed neural networks enable improved solution accuracy of the Navier-Stokes equations
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916546636414976 |
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| author | Roy, Nityananda Dürr, Robert Bück, Andreas Sundar, S. |
| author_facet | Roy, Nityananda Dürr, Robert Bück, Andreas Sundar, S. |
| contents | Generating an accurate solution of the Navier--Stokes equations using physics--informed neural networks (PINNs) for higher Reynolds numbers in the corners of a lid--driven cavity problem is challenging. In this paper, we improve the solution accuracy of the incompressible Navier--Stokes equations in the region near the walls significantly and generate accurate secondary vortices in the corners of the lid--driven cavity by solving the governing equations using finite difference--based PINNs (FD--PINNs) without employing the known solution. We adopt the domain decomposition method (DDM) and combine it with the FD--PINNs to solve the lid--driven cavity problem for the Reynolds numbers Re = 400 and Re=1000. A comparison of the mean square error (MSE) between the presented and standard FD--PINNs using the reference solution is exhibited, showing the accuracy and effectiveness of the new approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00014 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite difference physics-informed neural networks enable improved solution accuracy of the Navier-Stokes equations Roy, Nityananda Dürr, Robert Bück, Andreas Sundar, S. Computational Physics Fluid Dynamics Generating an accurate solution of the Navier--Stokes equations using physics--informed neural networks (PINNs) for higher Reynolds numbers in the corners of a lid--driven cavity problem is challenging. In this paper, we improve the solution accuracy of the incompressible Navier--Stokes equations in the region near the walls significantly and generate accurate secondary vortices in the corners of the lid--driven cavity by solving the governing equations using finite difference--based PINNs (FD--PINNs) without employing the known solution. We adopt the domain decomposition method (DDM) and combine it with the FD--PINNs to solve the lid--driven cavity problem for the Reynolds numbers Re = 400 and Re=1000. A comparison of the mean square error (MSE) between the presented and standard FD--PINNs using the reference solution is exhibited, showing the accuracy and effectiveness of the new approach. |
| title | Finite difference physics-informed neural networks enable improved solution accuracy of the Navier-Stokes equations |
| topic | Computational Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2501.00014 |