Numerical simulation of flows past flat plates using volume penalization

• Published in: Computational & Applied Mathematics Vol. 33; no. 2; pp. 481 - 495
• Main Authors: Schneider, Kai, Paget-Goy, Mickaël, Verga, Alberto, Farge, Marie
• Format: Journal Article
• Language: English
• Published: Basel Springer Basel 2014; Springer Verlag
• Subjects: Applications of Mathematics; Computational Mathematics and Numerical Analysis; Fluid Dynamics; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematics; Mathematics and Statistics; Physics; Computational methods in fluid dynamics; Wavelets; Vortex dynamics; Secondary 76D17; 65M70; Free shear layers; 65T60; Instability of shear layers; Spectral methods; Primary 65M85
• ISSN: 0101-8205; 1807-0302
• DOI: 10.1007/s40314-013-0076-9

We present numerical simulations of two-dimensional viscous incompressible flows past flat plates having different kind of wedges: one tip of the plate is rectangular, while the other tip is either a wedge with an angle of 30 ∘ or a round shape. We study the shear layer instability of the flow considering different scenarios, either an impulsively started plate or an uniformly accelerated plate, for Reynolds number R e = 9500 . The volume penalization method, with either a Fourier spectral or a wavelet discretization, is used to model the plate geometry with no-slip boundary conditions, where the geometry of the plate is simply described by a mask function. On both tips, we observe the formation of thin shear layers which are rolling up into spirals and form two primary vortices. The self-similar scaling of the spirals corresponds to the theoretical predictions of Saffman for the inviscid case. At later times, these vortices are advected downstream and the free shear layers undergo a secondary instability. We show that their formation and subsequent dynamics is highly sensitive to the shape of the tips. Finally, we also check the influence of a small riblet, added on the back of the plate on the flow evolution.