A time averaged steady state method for the Navier–Stokes equations,International Journal for Numerical Methods in Fluids

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A time averaged steady state method for the Navier–Stokes equations
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-02-10 , DOI: 10.1002/fld.4964
Mengjie Zhao ₁ , Rubén Zorrilla ₂ , Riccardo Rossi ₃ , Roland Wüchner ₄

Affiliation

This work derives an incompressible variational multiscales time-averaged Navier–Stokes (NS) formulation that aims at obtaining accurate steady state solutions. Rather than using the standard time instantaneous velocity and pressure, the new formulation devises a time averaging procedure based on rewriting and solving the NS equations in terms of the newly defined time-averaged velocity and pressure. Hence, the method could be understood as a convenient change of variable so that the problem is rewritten directly in terms of the steady state quantities. The important advantage of such a point of view is that it can in principle be applied to any other formulation. Such time averaging procedure is complemented by two time step modification strategies in order to accelerate the convergence to the steady state. The guidelines of an integrated framework are presented in the article, starting with the description of the proposed numerical technique applied to general incompressible flows. The explanation is enhanced with a one-dimensional (1D) nonlinear oscillator example. Several results are presented concerning analytical benchmarks, simulation of flows in laminar, transitional and turbulent regimes with and without an inherently steady solution.

中文翻译：

Navier-Stokes 方程的时间平均稳态方法

这项工作推导出了一个不可压缩的变分多尺度时间平均纳维-斯托克斯 (NS) 公式，旨在获得准确的稳态解。新公式不是使用标准的时间瞬时速度和压力，而是基于根据新定义的时间平均速度和压力重写和求解 NS 方程来设计时间平均程序。因此，该方法可以理解为变量的方便变化，从而直接根据稳态量重写问题。这种观点的重要优点是它原则上可以应用于任何其他公式。这种时间平均过程由两个时间步长修改策略补充，以加速收敛到稳态。文章中介绍了综合框架的指导方针，首先描述了适用于一般不可压缩流动的拟议数值技术。用一维 (1D) 非线性振荡器示例加强了解释。给出了一些关于分析基准、层流、过渡和湍流状态下的流动模拟的结果，有和没有固有的稳定解决方案。

更新日期：2021-02-10

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