An improved direct-forcing immersed-boundary method for finite difference applications

A modified immersed-boundary method is developed using the direct-forcing concept. An improved bilinear interpolation/extrapolation algorithm is implemented for more accurate boundary forcing expressions and easier implementation. Detailed discussions of the method are presented on the stability, velocity interpolation on the immersed boundary, direct-forcing extrapolation to the grid points, resolution of the immersed boundary points, and internal treatment. The method can achieve second-order accurate solutions. The method is then applied to a finite-difference scheme to compute flow over a stationary cylinder, an oscillating cylinder, and a stationary sphere. The accuracy of the computational results is verified using numerous computational and experimental results in the literature.