Application of RES methods for computation of hydrodynamic flows by an example of a 2D flow past a circular cylinder for Re = 5–200

An effective method of simulation of multidimensional hydrodynamic problems for small Mach numbers is described. The method is based on utilization of FFT (fast Fourier transform) for solving the Poisson equation on a rectangular grid in domains with complicated geometry (particularly multi-linked). Simulation was performed with zero numerical viscosity. The speed of calculation of the Poisson equation is 1–2 orders of magnitude higher compared to that of the calculation based on standard iteration techniques. Systematic simulations of a 2D flow past a cylinder in the channel with permeable and impermeable boundaries were performed. The critical values of the Re number of the onset of vortex movement (Re0) and loss of stability of steady (Re1) and two-dimensional movement (Re2) are estimated with high accuracy for the two cases mentioned.