We solve fluid flow problems through a space-time finite element method. The weak form of the Navier-Stokes equations is stabilized using the variational multi-scale formulation. The finite element problem is posed on the "full" space-time domain, considering time as another dimension. 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.

翻译：我们采用时空有限元方法求解流体流动问题。通过变分多尺度公式对纳维-斯托克斯方程的弱形式进行稳定化处理。该有限元问题在"全"时空域上提出，将时间视为另一个维度。我们将该方法应用于计算流体力学的两个基准问题：顶盖驱动方腔流和圆柱绕流。通过与现有文献结果的对比验证了本方法的有效性，并证明我们的方法能够求解极大空间时间块问题。