论文标题
非平稳stokes和Navier-Stokes问题的等几何残余最小化（IGRM）
Isogeometric Residual Minimization (iGRM) for Non-Stationary Stokes and Navier-Stokes Problems
论文作者
论文摘要
我们表明，可以为非平稳的Stokes和Navier-Stokes方程获得线性计算成本的求解器。我们的方法采用了Guermond和Minev开发的一种技术，该技术包括奇异扰动和分裂方案。尽管时间整合方案是隐式的，但我们使用有限元素来离散空间对应物。在每个时间阶段，我们仅在一个方向上求解具有弱衍生物的PDE（这允许线性计算成本），以牺牲这些PDE的右侧处理上一个时间步长解决方案的强二阶导数。这激发了使用平滑功能（例如B-Splines）的使用。对于较高的雷诺数字，其中一些PDE变得不稳定。为了强力处理这些不稳定性，我们建议使用残留的最小化技术。我们测试了制造解决方案以及腔流问题的问题。
We show that it is possible to obtain a linear computational cost FEM-based solver for non-stationary Stokes and Navier-Stokes equations. Our method employs a technique developed by Guermond and Minev, which consists of singular perturbation plus a splitting scheme. While the time-integration schemes are implicit, we use finite elements to discretize the spatial counterparts. At each time-step, we solve a PDE having weak-derivatives in one direction only (which allows for the linear computational cost), at the expense of handling strong second-order derivatives of the previous time step solution, on the right-hand side of these PDEs. This motivates the use of smooth functions such as B-splines. For high Reynolds numbers, some of these PDEs become unstable. To deal robustly with these instabilities, we propose to use a residual minimization technique. We test our method on problems having manufactured solutions, as well as on the cavity flow problem.
