An immersed boundary method with an approximate projection on nonstaggered grids to solve unsteady fluid flow with a submerged moving rigid object

An immersed boundary method is presented, which uses an approximate projection method on nonstaggered grids for computing flows with submerged and moving boundaries. The incompressible Navier–Stokes equations are discretized using a second-order accurate finite difference technique on a nonstaggered grid system, and the new immersed boundary method is proposed based on an approximate projection method with two pressure correction techniques, the Armfield method and the geometrical grid Reynolds modified method on nonstaggered grids. By using this method, the results obtained from (1) flow past a rigid cylinder in two dimensions with different Reynold numbers and (2) flow around an oscillatory circular cylinder in flow at low Keulegan–Carpenter numbers are in agreement with the reported experimental and numerical data, demonstrating that this convenient method of constraining the interface is a reliable and robust numerical approach for solving unsteady fluid flow with a submerged moving rigid object. This method has the advantage of using significantly less computation time and lower computation sources than the traditional immersed boundary methods.