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Adaptive modeling of turbulent flow with residual based turbulent kinetic energy dissipation

机译:基于残差的湍动能耗散的湍流自适应建模

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摘要

In this paper we first review our recent work on a new framework for adaptive turbulence simulation: we model turbulence by weak solutions to the Navier-Stokes equations that are wellposed with respect to mean value output in the form of functionals, and we use an adaptive finite element method to compute approximations with a posteriori error control based on the error in the functional output. We then derive a local energy estimate for a particular finite element method, which we connect to related work on dissipative weak Euler solutions with kinetic energy dissipation due to lack of local smoothness of the weak solutions. The ideas are illustrated by numerical results, where we observe a law of finite dissipation with respect to a decreasing mesh size.
机译:在本文中,我们首先回顾一下我们在自适应湍流仿真的新框架上的最新工作:我们通过对Navier-Stokes方程的弱解进行建模,这些方程相对于以函数形式的平均值输出而言是很好的,并且我们使用自适应基于后输出误差控制的有限元方法,基于函数输出中的误差进行后验误差控制。然后,我们导出特定有限元方法的局部能量估计,并将其与耗散的弱Euler解的相关工作联系起来,该动因由于弱解的局部光滑性而具有动能耗散。数值结果说明了这些思想,其中我们观察到关于减小的网格尺寸的有限耗散定律。

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