Data-driven shape inference in three-dimensional steady state supersonic flows using ODIL and JAX-Fluids
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915350323396608 |
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| author | Buhendwa, Aaron B. Bezgin, Deniz A. Karnakov, Petr Adams, Nikolaus A. Koumoutsakos, Petros |
| author_facet | Buhendwa, Aaron B. Bezgin, Deniz A. Karnakov, Petr Adams, Nikolaus A. Koumoutsakos, Petros |
| contents | We present a novel data- and first-principles-driven method for inferring the shape of a solid obstacle and its flow field in three-dimensional steady-state supersonic flows. The method combines the Optimizing a Discrete Loss (ODIL) technique with the automatically differentiable JAX-Fluids CFD solver to jointly reconstruct flow fields and obstacle shapes. ODIL minimizes the discrete residual of the governing PDE via gradient descent-based algorithms and inherits the consistency and stability of the chosen numerical discretization. Discrete residuals and their gradients are computed using JAX-Fluids, which features nonlinear shock-capturing schemes and level-set-based immersed solid boundaries. We validate our method on synthetic data for challenging inverse problems, including shape inference of solid obstacles in 3D steady-state supersonic flows. In particular, we study flow around a cylinder, sphere, and ellipse. Two shape representations are investigated: (1) parametric, where the shape is described by a small set of parameters (e.g., radius of the cylinder or sphere) optimized jointly with the flow field, and (2) free-form, where the level-set function is optimized pointwise over the mesh without predefined shapes. For the parametric case, we provide a detailed comparison with Physics-Informed Neural Networks. We demonstrate that the combination of nonlinear shock-capturing discretization and level-set-based interface representation enables accurate inference of obstacle shapes and flow fields via the ODIL method. This approach opens new avenues for solving complex inverse problems in supersonic aerodynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10094 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Data-driven shape inference in three-dimensional steady state supersonic flows using ODIL and JAX-Fluids Buhendwa, Aaron B. Bezgin, Deniz A. Karnakov, Petr Adams, Nikolaus A. Koumoutsakos, Petros Fluid Dynamics We present a novel data- and first-principles-driven method for inferring the shape of a solid obstacle and its flow field in three-dimensional steady-state supersonic flows. The method combines the Optimizing a Discrete Loss (ODIL) technique with the automatically differentiable JAX-Fluids CFD solver to jointly reconstruct flow fields and obstacle shapes. ODIL minimizes the discrete residual of the governing PDE via gradient descent-based algorithms and inherits the consistency and stability of the chosen numerical discretization. Discrete residuals and their gradients are computed using JAX-Fluids, which features nonlinear shock-capturing schemes and level-set-based immersed solid boundaries. We validate our method on synthetic data for challenging inverse problems, including shape inference of solid obstacles in 3D steady-state supersonic flows. In particular, we study flow around a cylinder, sphere, and ellipse. Two shape representations are investigated: (1) parametric, where the shape is described by a small set of parameters (e.g., radius of the cylinder or sphere) optimized jointly with the flow field, and (2) free-form, where the level-set function is optimized pointwise over the mesh without predefined shapes. For the parametric case, we provide a detailed comparison with Physics-Informed Neural Networks. We demonstrate that the combination of nonlinear shock-capturing discretization and level-set-based interface representation enables accurate inference of obstacle shapes and flow fields via the ODIL method. This approach opens new avenues for solving complex inverse problems in supersonic aerodynamics. |
| title | Data-driven shape inference in three-dimensional steady state supersonic flows using ODIL and JAX-Fluids |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2408.10094 |