Solving fluid flow problems in space-time with multiscale stabilization: formulation and examples
Numerical Analysis
2024-11-25 v3 Numerical Analysis
Analysis of PDEs
Abstract
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.
Cite
@article{arxiv.2402.12571,
title = {Solving fluid flow problems in space-time with multiscale stabilization: formulation and examples},
author = {Biswajit Khara and Robert Dyja and Kumar Saurabh and Anupam Sharma and Baskar Ganapathysubramanian},
journal= {arXiv preprint arXiv:2402.12571},
year = {2024}
}