...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Journal of Computational Physics >Efficient computation of the spectrum of viscoelastic flows
【24h】

Efficient computation of the spectrum of viscoelastic flows

机译：粘弹性流动谱的高效计算

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

The understanding of viscoelastic flows in many situations requires not only the steady state Solution of the governing equations, but also its sensitivity to small perturbations. Linear stability analysis leads to a generalized eigenvalue problem (GEVP), whose numerical analysis may be challenging, even for Newtonian liquids, because the incompressibility constraint creates singularities that lead to non-physical eigenvalues at infinity. For viscoelastic flows, the difficulties increase due to the presence of continuous spectrum, related to the constitutive equations. The Couette How of upper convected Maxwell (UCM) liquids has been used as a case Study of the stability of viscoelastic flows. The spectrum consists of two discrete eigenvalues and a continuous segment with real part equal to - 1/We (We is the Weissenberg number). Most of the approximations in the literature were obtained using spectral expansions. The eigenvalues close to the continuous part of the spectrum show very slow convergence. In this work, the linear stability of Couette flow of a UCM liquid is studied using a finite element method. A new procedure to eliminate the eigenvalues at infinity from the GEVP is proposed. The procedure takes advantage of the Structure of the matrices involved and avoids the computational overhead of the Usual mapping techniques. The GEVP is transformed into a non-degenerate GEVP of dimension five times smaller. The computed eigen-functions related to the continuous spectrum are in good agreement with the analytic solutions obtained by Graham [M.D. Graharn, Effect of axial flow on viscoelastic Taylor-Couette instability, J. Fluid Mech. 360 (1998) 341]. (C) 2008 Elsevier Inc. All rights reserved.
机译：在许多情况下，对粘弹性流的理解不仅需要控制方程的稳态解，还需要其对小扰动的敏感性。线性稳定性分析会导致广义特征值问题（GEVP），即使对于牛顿液体，其数值分析也可能具有挑战性，因为不可压缩性约束会产生奇异性，从而导致无穷大的非物理特征值。对于粘弹性流，由于存在与本构方程有关的连续频谱，因此难度增加。上部对流麦克斯韦（UCM）液体的Couette How已用作粘弹性流动稳定性的案例研究。频谱由两个离散特征值和一个连续部分组成，其实际部分等于-1 / We（我们是Weissenberg数）。文献中的大多数近似值都是使用频谱扩展获得的。接近频谱连续部分的特征值显示非常缓慢的收敛。在这项工作中，使用有限元方法研究了UCM液体的Couette流的线性稳定性。提出了一种从GEVP中消除无穷大特征值的新方法。该过程利用了所涉及的矩阵的结构，并且避免了常规映射技术的计算开销。将GEVP转换为尺寸较小的非退化GEVP的五倍。计算出的与连续光谱有关的本征函数与Graham [M.D. Graharn，《轴向流动对粘弹性Taylor-Couette不稳定性的影响》，J。Fluid Mech。 360（1998）341]。 （C）2008 Elsevier Inc.保留所有权利。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号