Local projection stabilization for the Oseen problem
Local projection stabilization for the Oseen problem
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DOI：
10.1093/imanum/drv032
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发表时间：
2016-04
影响因子：
2.1
通讯作者：
Helene Dallmann;D. Arndt;G. Lube
中科院分区：
文献类型：
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作者：
Helene Dallmann;D. Arndt;G. Lube
考虑了速度和压力具有非超稳定近似的含时Osen问题的协调有限元近似。这项工作作为不可压Navier-Stokes问题的初步研究。在高雷诺数的情况下，局部投影稳定化方法被认为是。特别是，流线迎风的想法与无发散约束的稳定相结合。对于所产生的半离散问题，给出了稳定性和收敛性分析。我们的方法改进了Matthies & Tobiska（2014，IMA J. Numer.分析：35，239-269）。最后，我们将该方法应用于含时不可压Navier-Stokes问题，测试了方法的精度，并进行了简单边界层和分离的数值实验。
We consider conforming finite element approximations of the time-dependent Oseen problem with inf–sup stable approximation of velocity and pressure. The work serves as a preliminary study of the incompressible Navier–Stokes problem. In the case of high Reynolds numbers, the local projection stabilization method is considered. In particular, the idea of streamline upwinding is combined with stabilization of the divergence-free constraint. For the arising semidiscrete problem, a stability and convergence analysis is given. Our approach improves some results of a recent paper by Matthies & Tobiska (2014,IMA J. Numer. Anal.,35, 239–269). Finally, we apply the approach to the time-dependent incompressible Navier–Stokes problem, test the accuracy of the method and conduct numerical experiments with simple boundary layers and separation.