Addressing complex boundary conditions of miscible flow and transport in two and three dimensions with application to optimal control
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916169981624320 |
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| author | Li, Yiqun Wang, Hong Zheng, Xiangcheng |
| author_facet | Li, Yiqun Wang, Hong Zheng, Xiangcheng |
| contents | We investigate complex boundary conditions of the miscible displacement system in two and three space dimensions with the commonly-used Bear-Scheidegger diffusion-dispersion tensor, which describes, e.g., the porous medium flow processes in petroleum reservoir simulation or groundwater contaminant transport. Specifically, we incorporate the no-flux boundary condition for the Darcy velocity to prove that the general no-flux boundary condition for the transport equation is equivalent to the normal derivative boundary condition of the concentration, based on which we further prove several complex boundary conditions by the Bear-Scheidegger tensor and its derivative. The derived boundary conditions not only provide new insights and distinct properties of the Bear-Scheidegger diffusion-dispersion tensor, but accommodate the coupling and the nonlinearity of the miscible displacement system and the Bear-Scheidegger tensor in deriving the first-order optimality condition of the corresponding optimal control problem for practical application. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14079 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Addressing complex boundary conditions of miscible flow and transport in two and three dimensions with application to optimal control Li, Yiqun Wang, Hong Zheng, Xiangcheng Optimization and Control 35K20, 49J20, 49K20, 76S05 We investigate complex boundary conditions of the miscible displacement system in two and three space dimensions with the commonly-used Bear-Scheidegger diffusion-dispersion tensor, which describes, e.g., the porous medium flow processes in petroleum reservoir simulation or groundwater contaminant transport. Specifically, we incorporate the no-flux boundary condition for the Darcy velocity to prove that the general no-flux boundary condition for the transport equation is equivalent to the normal derivative boundary condition of the concentration, based on which we further prove several complex boundary conditions by the Bear-Scheidegger tensor and its derivative. The derived boundary conditions not only provide new insights and distinct properties of the Bear-Scheidegger diffusion-dispersion tensor, but accommodate the coupling and the nonlinearity of the miscible displacement system and the Bear-Scheidegger tensor in deriving the first-order optimality condition of the corresponding optimal control problem for practical application. |
| title | Addressing complex boundary conditions of miscible flow and transport in two and three dimensions with application to optimal control |
| topic | Optimization and Control 35K20, 49J20, 49K20, 76S05 |
| url | https://arxiv.org/abs/2403.14079 |