Numerical simulation of two-dimensional flows over a circular cylinder using the immersed boundary method

In this work, a virtual boundary method is applied to the numerical simulation of a uniform flow over a cylinder. The force source term, added to the two-dimensional Navier–Stokes equations, guarantees the imposition of the no-slip boundary condition over the body–fluid interface. These equations are discretized, using the finite differences method. The immersed boundary is represented with a finite number of Lagrangian points, distributed over the solid–fluid interface. A Cartesian grid is used to solve the fluid flow equations. The key idea is to propose a method to calculate the interfacial force without ad hoc constants that should usually be adjusted for the type of flow and the type of the numerical method, when this kind of model is used. In the present work, this force is calculated using the Navier–Stokes equations applied to the Lagrangian points and then distributed over the Eulerian grid. The main advantage of this approach is that it enables calculation of this force field, even if the interface is moving or deforming. It is unnecessary to locate the Eulerian grid points near this immersed boundary. The lift and drag coefficients and the Strouhal number, calculated for an immersed cylinder, are compared with previous experimental and numerical results, for different Reynolds numbers.