A numerical method for simulating flow involving moving boundaries with high order accuracy

To simulate a flow involving moving boundaries accurately and efficiently, this paper presents a numerical method for the simulation of moving boundary problems with a feedback force which is used to represent the effects of rigid boundaries. The method uses the movements of feedback forces to represent moving boundaries on a cartesian grid. The central difference scheme is corrected by incorporating the jump conditions of velocities and pressure to achieve second-order accuracy and the incompressible Navier-Stokes equation is solved. In addition, suitable methods for the construction of feedback forces and velocity interpolation on the boundaries are presented. Using this method, the paper simulated a flow passing a stationary cylinder and the flows subjected to an oscillating cylinder and a flapping insect wing at low Reynolds numbers. The results are consistent with previous numerical and experimental work. They show that the method is as efficient as Peskin's immersed boundary method when dealing with moving boundaries, but it achieves a higher-order of accuracy.