Application of variable period time spectral method to unsteady flow around rectangular cylinder

Based on the characteristic of time periodic unsteady flow, the time spectral method was applied to two-dimensional incompressible laminar flow around a rectangular cylinder in infinite medium at low Reynolds numbers. A variable time period method based on residual gradients was combined to iterate the variables and time period simultaneously because of the unknown time period of flow around the cylinder. The accuracy and convergence rate of the time spectral method were investigated and the influence of different parameters on the final results was analyzed. The results show that the present method could simulate the vortex shedding phenomenon accurately and the time cost could decrease to 10%-25% of that of the conventional dual time stepping method based on the finite difference scheme. The Strouhal number and drag characteristics confirm the feasibility of the present method. Our results indicate that the variable time period method is insensitive to parameter selection and can predict the time period accurately.