近似反褶积模型的建模误差
Modeling error in Approximate Deconvolution Models
摘要：
研究了三维周期情况下近似反褶积模型的建模误差在反褶积阶数$N$变为$\infty$时的渐近行为。我们认为顺序顺序的广义Helmholz滤波器的$p$和高斯滤波器。对于Helmholz滤波器，我们估计收敛到零的速度由于能量预算，Gronwall引理和尖锐的不等式傅立叶系数的残余应力。接下来，我们将展示为什么相同的分析不允许在高斯滤波器的情况下得出收敛到零的误差建模的结论，留下未决问题。
英文摘要：
We investigate the assymptotic behaviour of the modeling error in approximate deconvolution model in the 3D periodic case, when the order $N$ of deconvolution goes to $\infty$. We consider successively the generalised Helmholz filters of order $p$ and the Gaussian filter. For Helmholz filters, we estimate the rate of convergence to zero thanks to energy budgets, Gronwall's Lemma and sharp inequalities about Fouriers coefficients of the residual stress. We next show why the same analysis does not allow to conclude convergence to zero of the error modeling in the case of Gaussian filter, leaving open issues.
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