论文标题
条件良好的超球和光谱整合方法，用于分解牛顿和粘弹性流体的通道流量
Well-conditioned ultraspherical and spectral integration methods for resolvent analysis of channel flows of Newtonian and viscoelastic fluids
论文作者
论文摘要
流体流的模态和非模式分析提供了对湍流过渡早期阶段的基本见解。动力发电机的特征值控制了各个模式的时间生长或衰减，而频率响应操作员的单数值量化了线性稳定流的干扰的扩增。在本文中，我们开发了良好的超球和光谱整合方法，用于对牛顿和粘弹性流体的通道流的频率响应分析。即使对良好的条件进行了离散化方法，我们也证明，如果将奇异值计算为频率响应操作员及其伴随的级联连接的特征值，则计算可能是错误的。为了解决此问题，我们利用频率响应操作员与其伴随的反馈互连，以避免计算倒置并促进稳健的单数值分解。具体而言，与常规光谱搭配方法相反，提出的方法（i）在高魏森伯格数字的粘弹性流体的通道流中产生可靠的结果（$ \ sim 500 $）； （ii）对于原始变量中的方程式不需要交错的网格。
Modal and nonmodal analyses of fluid flows provide fundamental insight into the early stages of transition to turbulence. Eigenvalues of the dynamical generator govern temporal growth or decay of individual modes, while singular values of the frequency response operator quantify the amplification of disturbances for linearly stable flows. In this paper, we develop well-conditioned ultraspherical and spectral integration methods for frequency response analysis of channel flows of Newtonian and viscoelastic fluids. Even if a discretization method is well-conditioned, we demonstrate that calculations can be erroneous if singular values are computed as the eigenvalues of a cascade connection of the frequency response operator and its adjoint. To address this issue, we utilize a feedback interconnection of the frequency response operator with its adjoint to avoid computation of inverses and facilitate robust singular value decomposition. Specifically, in contrast to conventional spectral collocation methods, the proposed method (i) produces reliable results in channel flows of viscoelastic fluids at high Weissenberg numbers ($\sim 500$); and (ii) does not require a staggered grid for the equations in primitive variables.
