滤波Navier-斯托克斯方程近似反褶积模型的收敛性
Convergence of approximate deconvolution models to the filtered Navier-Stokes Equations
摘要：
我们考虑一个三维近似反卷积模型（ADM），它属于大涡模拟（LES）模型。我们的工作与周期边界条件和过滤器，用于平均流体方程是亥姆霍兹之一。我们证明了存在性和唯一性，我们称之为"定期弱"解决方案$(\wit_N,q_N)$的模型，任何固定的顺序$N\in\N$的反卷积。然后，我们证明了序列$\{(\wit_N,q_N)\}_{N \in \N}$收敛-在某种意义上-过滤Navier-斯托克斯方程的解决方案，因为$N$走向无穷大。这严格地表明，类ADM模型，我们认为有最有意义的近似性能的平均值的Navier-斯托克斯方程的解决方案。
英文摘要：
We consider a 3D Approximate Deconvolution Model (ADM) which belongs to the class of Large Eddy Simulation (LES) models. We work with periodic boundary conditions and the filter that is used to average the fluid equations is the Helmholtz one. We prove existence and uniqueness of what we call a "regular weak" solution $(\wit_N,q_N)$ to the model, for any fixed order $N\in\N$ of deconvolution. Then, we prove that the sequence $\{(\wit_N,q_N)\}_{N \in \N}$ converges -in some sense- to a solution of the filtered Navier-Stokes equations, as $N$ goes to infinity. This rigorously shows that the class of ADM models we consider have the most meaningful approximation property for averages of solutions of the Navier-Stokes equations.
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