With the aid of direct numerical simulation, this paper presents a detailed investigation on the flow around a finite square cylinder at a fixed aspect ratio (AR) of 4 and six Reynolds numbers (Re = 50, 100, 150, 250, 500, and 1000). It is found that the mean streamwise vortex structure is also affected by Re, apart from the AR value. Three types of mean streamwise vortices have been identified and analyzed in detail, namely, “Quadrupole Type” at Re = 50 and Re = 100, “Six-Vortices Type” at Re = 150 and Re = 250, and “Dipole Type” at Re = 500 and Re = 1000. It is the first time that the “Six-Vortices Type” mean streamwise vortices are reported, which is considered as a transitional structure between the other two types. Besides, three kinds of spanwise vortex-shedding models have been observed in this study, namely, “Hairpin Vortex Model” at Re = 150, “C and Reverse-C and Hairpin Vortex Model (Symmetric Shedding)” at Re = 250, and “C and Reverse-C and Hairpin Vortex Model (Symmetric/Antisymmetric Shedding)” at Re = 500 and Re = 1000. The newly proposed “C and Reverse-C and Hairpin Vortex Model” shares some similarities with “Wang’s Model” [H. F. Wang and Y. Zhou, “The finite-length square cylinder near wake,” J. Fluid Mech. 638, 453–490 (2009)] but differs in aspects such as the absence of the connection line near the free-end and the “C-Shape” vortex structure in the early stage of the formation of the spanwise vortex.

This paper presents an extensive review of most of the existing TVD schemes found in literature that are based on the One-step Time-space-coupled Unsteady TVD criterion (OTU-TVD), the Multi-step Time-space-separated Unsteady TVD criterion (MTU-TVD) and the Semi-discrete Steady-state TVD criterion (SS-TVD). The design principles of these schemes are examined in detail. It is found that the selection of appropriate flux-limiters is a key design element in developing these schemes. Different flux-limiter forms (CFL-dependent or CFL-independent, and various limiting criteria) are shown to lead to different performances in accuracy and convergence. Furthermore, a refined SS-TVD flux-limiter, referred to henceforth as TCDF (Third-order Continuously Differentiable Function), is proposed for steadystate calculations based on the review. To evaluate the performance of the newly proposed scheme, many existing classical SS-TVD limiters are compared with the TCDF in eight two-dimensional test cases. The numerical results clearly show that the TCDF results in an improved overall performance.

This paper presents a new volume-of-fluid scheme (M-CICSAM), capable of capturing abrupt interfaces on meshes of arbitrary topology, which is a modification to the Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM) proposed in the recent literature. Without resort to any explicit interface reconstruction, M-CICSAM is able to precisely model the complex free surface deformation, such as interface rupture and coalescence. By theoretical analysis, it is shown that the modified CICSAM overcomes three inherent drawbacks of the original CICSAM, concerning the basic differencing schemes, the switching strategy between the compressive downwind and diffusive high-resolution schemes, and the far-upwind reconstruction technique on arbitrary unstructured meshes. To evaluate the performance of the newly proposed scheme, several classic interface capturing methods developed in the past decades are compared with M-CICSAM. The numerical results clearly demonstrate that M-CICSAM produces more accurate predictions on arbitrary meshes, especially at high Courant numbers, by reducing the numerical diffusion and preserving the interface shape. Keywords: two-phase flows; interface capturing; unstructured meshes; volume of fluid (VOF); normalized variable diagram (NVD); normalized variable and space formulation (NVSF)

SUMMARYThree new far‐upwind reconstruction techniques, New‐Technique 1, 2, and 3, are proposed in this paper, which localize the normalized variable and space formulation (NVSF) schemes and facilitate the implementation of standard bounded high‐resolution differencing schemes on arbitrary unstructured meshes. By theoretical analysis, it is concluded that the three new techniques overcome two inherent drawbacks of the original technique found in the literature. Eleven classic high‐resolution NVSF schemes developed in the past decades are selected to evaluate performances of the three new techniques relative to the original technique. Under the circumstances of arbitrary unstructured meshes, stretched meshes, and uniform triangular meshes, for each NVSF scheme, the accuracies and convergence properties, when implementing the four aforementioned far‐upwind reconstruction techniques respectively, are assessed by the pure convection of several scalar profiles. The numerical results clearly show that New‐Technique‐2 leads to a better performance in terms of overall accuracy and convergence behavior for the 11 NVSF schemes. Copyright © 2013 John Wiley & Sons, Ltd.

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SUMMARYA refined r-factor algorithm for implementing total variation diminishing (TVD) schemes on arbitrary unstructured meshes, referred to henceforth as a face-perpendicular far-upwind interpolation scheme for arbitrary meshes (FFISAM), is proposed based on an extensive review of the existing r-factor algorithms available in the literature. The design principles, as well as the respective advantages and disadvantages, of the existing algorithms are first systematically analyzed before presenting the FFISAM. The FFISAM is designed to combine the merits of various existing r-factor algorithms. The performance of the FFISAM, implemented in 10 classical TVD schemes, is evaluated against four two-dimensional pure-advection benchmark test cases where analytical solutions are available. The numerical results clearly show that the FFISAM leads to a better overall performance than the existing algorithms in terms of accuracy and convergence on arbitrary unstructured meshes for the 10 classical TVD schemes.

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RANS simulations are performed for flow past rectangular cylinders with different elongation ratios (L/D=1, 2, 4, 6, 8, 10, 12, 14 and 16) at Re=22000 using the k-ω SST turbulence model. As L/D increases from 1 to 6, stepwise increase of Strouhal number (St) exists, whereas an almost linear variation of St with respect to L/D can be found (St=0.1618*L/D) at L/D≥8. In the flow, two small secondary vortices beneath the shear layers are identified and the trailing-edge secondary vortex presents opposite rotational direction comparing with the leading-edge main vortex. Analysis of the shear layer and vortex characteristics is carried out to correlate with the wall normal stress and shear stress on the rectangular cylinder surfaces. Further, four coupling modes between leading-edge vortex (L-vortex) and trailing-edge vortex (T-vortex) among cylinders with different L/D are observed, named L-Vortex Mode (i.e. L/D=1~2), L-T-Vortex Mode (i.e. L/D=4~8), T-L-Vortex Mode (i.e. L/D=10~14), and T-Vortex Mode (i.e. L/D≥16). When L/D>4, the convective velocity of the L- and T-vortex is not sensitive to the L/D.