Solving fluid flow problems in space-time with multiscale stabilization: formulation and examples
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912129375797248 |
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| author | Khara, Biswajit Dyja, Robert Saurabh, Kumar Sharma, Anupam Ganapathysubramanian, Baskar |
| author_facet | Khara, Biswajit Dyja, Robert Saurabh, Kumar Sharma, Anupam Ganapathysubramanian, Baskar |
| contents | We present a space-time continuous-Galerkin finite element method for solving incompressible Navier-Stokes equations. To ensure stability of the discrete variational problem, we apply ideas from the variational multi-scale method. The finite element problem is posed on the ``full" space-time domain, considering time as another dimension. We provide a rigorous analysis of the stability and convergence of the stabilized formulation. And finally, we apply this method on two benchmark problems in computational fluid dynamics, namely, lid-driven cavity flow and flow past a circular cylinder. We validate the current method with existing results from literature and show that very large space-time blocks can be solved using our approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12571 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solving fluid flow problems in space-time with multiscale stabilization: formulation and examples Khara, Biswajit Dyja, Robert Saurabh, Kumar Sharma, Anupam Ganapathysubramanian, Baskar Numerical Analysis Analysis of PDEs We present a space-time continuous-Galerkin finite element method for solving incompressible Navier-Stokes equations. To ensure stability of the discrete variational problem, we apply ideas from the variational multi-scale method. The finite element problem is posed on the ``full" space-time domain, considering time as another dimension. We provide a rigorous analysis of the stability and convergence of the stabilized formulation. And finally, we apply this method on two benchmark problems in computational fluid dynamics, namely, lid-driven cavity flow and flow past a circular cylinder. We validate the current method with existing results from literature and show that very large space-time blocks can be solved using our approach. |
| title | Solving fluid flow problems in space-time with multiscale stabilization: formulation and examples |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2402.12571 |