Navier-Stokes方程牵引边界条件下的压力校正方案稳定性分析
Stability analysis of pressure correction schemes for the Navier-Stokes equations with traction boundary conditions
AI总结：
本文分析了两种旋转压力校正方案在开放和牵引边界条件下的稳定性，证明了改进方案在合适参数下无条件稳定，同时建立了边界校正方案的条件稳定性结果。
摘要：
我们为两种不同的旋转压力校正方案提供了稳定性分析，包括开放和牵引边界条件。首先，我们对[A. Bonito, J.-L. Guermond, and S. Lee. Modified pressure-correction projection methods: Open boundary and variable time stepping. In Numerical Mathematics and Advanced Applications - ENUMATH 2013, volume 103 of Lecture Notes in Computational Science and Engineering, pages 623-631. Springer, 2015]中的旋转梯度-散度稳定化方案进行了稳定性分析，证明在合适稳定参数下该方案无条件稳定。我们还建立了[E. Bansch. A finite element pressure correction scheme for the Navier-Stokes equations with traction boundary condition. Comput. Methods Appl. Mech. Engrg., 279:198-211, 2014]中提出的边界校正方案的条件稳定性结果。这些结果通过稳定化 gauge Uzawa 方法与具有牵引边界条件的旋转压力校正方案之间的等价性来证明。
英文摘要：
We present a stability analysis for two different rotational pressure correction schemes with open and traction boundary conditions. First, we provide a stability analysis for a rotational version of the grad-div stabilized scheme of [A. Bonito, J.-L. Guermond, and S. Lee. Modified pressure-correction projection methods: Open boundary and variable time stepping. In Numerical Mathematics and Advanced Applications - ENUMATH 2013, volume 103 of Lecture Notes in Computational Science and Engineering, pages 623-631. Springer, 2015]. This scheme turns out to be unconditionally stable, provided the stabilization parameter is suitably chosen. We also establish a conditional stability result for the boundary correction scheme presented in [E. Bansch. A finite element pressure correction scheme for the Navier-Stokes equations with traction boundary condition. Comput. Methods Appl. Mech. Engrg., 279:198-211, 2014]. These results are shown by employing the equivalence between stabilized gauge Uzawa methods and rotational pressure correction schemes with traction boundary conditions.
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