Numerical analysis of modular regularization methods for the BDF2 time discretization of the Navier-Stokes equations ∗
Numerical analysis of modular regularization methods for the BDF2 time discretization of the Navier-Stokes equations ∗
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DOI：
10.1051/m2an/2013120
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发表时间：
2014-05
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影响因子：
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通讯作者：
W. Layton;Nathaniel Mays;M. Neda;C. Trenchea
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文献类型：
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作者：
W. Layton;Nathaniel Mays;M. Neda;C. Trenchea
我们考虑一个解耦的，模块化的正则化算法近似的Navier-Stokes方程。该方法是：步骤1.1：将NSE推进一个时间步长，步骤1.1：正则化以获得新时间水平的近似。之前对该方法的分析是针对步骤1.1中的特定时间步进方法和步骤1.1中的简单稳定化。在本报告中，我们将解耦模块化稳定的数学支持扩展到（i）步骤1.1中更复杂且性能更好的BDF 2时间离散化，以及（ii）步骤1.1中更一般的（线性或非线性）正则化算子。我们给出了一个完整的稳定性分析，推导出条件的步骤1.1正则化算子的组合具有良好的稳定效果，特征的数值耗散引起的步骤1.1，证明了一个渐近误差估计，包括步骤1.1中使用的方法的数值误差和步骤1.1中的正则化一致性误差，并提供数值测试。
We consider an uncoupled, modular regularization algorithm for approximation of the Navier-Stokes equations. The method is: Step 1.1: Advance the NSE one time step, Step 1.1: Regularize to obtain the approximation at the new time level. Previous analysis of this approach has been for specific time stepping methods in Step 1.1 and simple stabilizations in Step 1.1. In this report we extend the mathematical support for uncoupled, modular stabilization to (i) the more complex and better performing BDF2 time discretization in Step 1.1, and (ii) more general (linear or nonlinear) regularization operators in Step 1.1. We give a complete stability analysis, derive conditions on the Step 1.1 regularization operator for which the combination has good stabilization effects, characterize the numerical dissipation induced by Step 1.1, prove an asymptotic error estimate incorporating the numerical error of the method used in Step 1.1 and the regularizations consistency error in Step 1.1 and provide numerical tests.