Linear Stability of Plane Couette Flow at Moderate Reynolds Numbers

The linear stability of plane Couette flow is studied by using a symbolic computation package (Mathematica). The power series method is used to obtain the solution of the Orr-Sommerfeld equation. This solution shows that plane Couette flow is unstable.La stabilité linéaire du flux de Couette sur un plan est étudiée par l'intermédiane d'un outil de calcul symbolic (Mathematica). La méthods de série de puissance est utilisée pour obtenir la solution de l'équation de Orr-Sommerfeld. Cette solution montre que le flux de Couette sur un plan est instable

Online Projective Integral with Proper Orthogonal Decomposition for Incompressible Flows Past NACA0012 Airfoil

The projective integration method based on the Galerkin-free framework with the assistance of proper orthogonal decomposition (POD) is presented in this paper. The present method is applied to simulate two-dimensional incompressible fluid flows past the NACA0012 airfoil problem. The approach consists of using high-accuracy direct numerical simulations over short time intervals, from which POD modes are extracted for approximating the dynamics of the primary variables. The solution is then projected with larger time steps using any standard time integrator, without the need to recompute it from the governing equations. This is called the online projective integration method. The results by the projective integration method are in good agreement with the full scale simulation with less computational needs. We also study the individual function of each POD mode used in the projective integration method. It is found that the first POD mode can capture basic flow behaviors but the overall dynamic is rather inaccurate. The second and the third POD modes assist the first mode by correcting magnitudes and phases of vorticity fields. However, adding the fifth POD mode in the model leads to some incorrect results in phase-shift forms for both drag and lift coefficients. This suggests the optimal number of POD modes to use in the projective integration method

Electronic cleansing in computed tomography colonography using AT layer identification with integration of gradient directional second derivative and material fraction model

Abstract Background In computed tomography colonography images, electronic cleansing (EC) is applied to remove opacified residual materials, called fecal-tagging materials (FTM), using positive-contrast tagging agents and laxative to facilitate polyp detection. Methods The proposed EC, EC prop , integrates the gradient directional second derivative into material fraction model to preserve submerged soft tissue (ST) under FTM. Three-material fraction model is used to remove FTM and artifacts at air-tagging (AT) layers and T-junctions where air, ST, and FTM material meet simultaneously. Moreover, the proposed AT layer identification is used to distinguish AT layers from air-tissue-tagging (ATT) layers in order to preserve ATT layers during cleansing. The clinical evaluation on 467 3-Dimensional band view images was conducted by the abdominal radiologist using four grading levels of cleansing quality with five causes of low quality EC. The amount of the remaining artifacts at T-junctions was approximated from the results of EC prop . The results from EC prop were compared with the results from syngo.via Client 3.0 Software, EC syngo , and the fast three-material modeling, EC prev , using the preference of the radiologist. Two-tailed paired Wilcoxon signed rank test is used to indicate statistical significance. Results The average grade on cleansing quality is 2.89 out of 4. The artifacts at T-junctions from 86.94% of the test images can be removed, whereas artifacts at T-junctions from only 13.06% of the test images cannot be removed. For 13.06% of the test images, the results from EC prop are more preferable to the results from EC syngo (p<0.008). For all the test images, the results from EC prop are more preferable to the results from EC prev (p<0.001). Finally, the visual assessment shows that EC prop can preserve ATT layers, submerged polyps and folds while EC prev can preserve only submerged folds but fails to preserve ATT layers. Conclusion From our implementation, EC prop can improve the performance of the existing EC, such that it can preserve ST, especially ATT layers and remove the artifacts at T-junctions which have never been proposed by any other methods before