Solving fluid flow problems in space-time with multiscale stabilization: formulation and examples
<|reference_start|>Solving fluid flow problems in space-time with multiscale stabilization: formulation and examples: 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.<|reference_end|>
@article{khara2024solving,
    title={Solving fluid flow problems in space-time with multiscale stabilization:
  formulation and examples},
    author={Biswajit Khara, Robert Dyja, Kumar Saurabh, Anupam Sharma, Baskar
  Ganapathysubramanian},
    journal={arXiv preprint arXiv:2402.12571},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.12571},
    primaryClass={math.NA cs.NA math.AP}
}