A Spectral Vanishing Viscosity Method for Large-Eddy Simulations
A Spectral Vanishing Viscosity Method for Large-Eddy Simulations
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DOI：
10.1006/jcph.2000.6552
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发表时间：
2000-09
影响因子：
4.1
通讯作者：
G. Karamanos;G. Karniadakis
中科院分区：
文献类型：
--
作者：
G. Karamanos;G. Karniadakis
开发了一种用于高雷诺数湍流的新模拟方法，它将非线性守恒定律中的单调性概念与大涡模拟概念相结合。由E. Tadmor在《SIAM J. Numer. Anal.》26卷30页（1989年）首次提出的谱消失粘性（SVV）被纳入纳维 - 斯托克斯方程以控制高波数振荡。与超粘性核不同，SVV方法涉及一个二阶算子，它可以很容易地在标准有限元代码中实现。在此呈现的工作中，使用分层谱/ hp方法进行离散化，有效地适应了从头开始的内在尺度分离。关键结果是通过SVV强制实现单调性，从而在不牺牲所提出离散化的形式精度（即指数收敛）的情况下实现稳定离散化。给出了几个例子来证明新方法的有效性，包括与湍流槽道流的涡粘性谱大涡模拟进行比较。在其当前的实现中，用于控制小尺度的SVV方法与大尺度是解耦的，但提出了一种将提供类似于经典大涡模拟公式的耦合的程序。
A new simulation approach for high Reynolds number turbulent flows is developed, combining concepts of monotonicity in nonlinear conservation laws with concepts of large-eddy simulation. The spectral vanishing viscosity (SVV), first introduced by E. Tadmor SIAM J. Numer. Anal.26, 30 (1989), is incorporated into the Navier?Stokes equations for controlling high-wavenumber oscillations. Unlike hyperviscosity kernels, the SVV approach involves a second-order operator which can be readily implemented in standard finite element codes. In the work presented here, discretization is performed using hierarchical spectral/hp methods accommodating effectively an ab initio intrinsic scale separation. The key result is that monotonicity is enforced via SVV leading to stable discretizations without sacrificing the formal accuracy, i.e., exponential convergence, in the proposed discretization. Several examples are presented to demonstrate the effectiveness of the new approach including a comparison with eddy-viscosity spectral LES of turbulent channel flow. In its current implementation the SVV approach for controlling the small scales is decoupled from the large scales, but a procedure is proposed that will provide coupling similar to the classical LES formulation.