Flow over two side-by-side square cylinders by CBS finite element scheme of Spalart–Allmaras model

In this study, the Characteristic-based-split (CBS) finite element scheme of Spalart–Allmaras (SA) model is presented. Under the framework of fractional step method, both the convection and diffusion terms in the Navier–Stokes equation and in the transportation equation are semi-implicitly treated. The numerical code is tested and compared using the 2-D benchmark problem of a flow past an isolated square cylinder at Re=22,000 with flow incidence angle of α=0°, then applied to the cross-flow around two square cylinders with side-by-side arrangement at the same Re. The spacing ratio between the two cylinders ranges between 1.5 and 3.5 and is found to have significant effects on flow patterns. Three patterns, the single-bluff body, the gap–flow interference, and the anti-phase synchronized patterns, are obtained by the CBS-SA scheme, which are compared closely with the findings from other publications. Meanwhile, the characteristics of the aerodynamic coefficients and the pressure coefficients for the cylinders are investigated. The Strouhal number, St, the two cylinders are over estimated, but the trend of St-L/D relationship agrees with those in previous studies. •The CBS finite element scheme of the Spalart–Allmaras model is shown•The numerical code is compared with other works for flow past a square cylinder•Flow past two side-by-side square cylinders at Re=22,000 is investigated•Three wake patterns are observed and compared with experiment from a reference•The St is overestimated but the trend of St-L/D agrees well with the references