An immersed boundary method for nonuniform grids

We propose a new direct forcing immersed boundary method for simulating the flow around an arbitrarily shaped body in nonuniform grids. A new formulation of the weight function for the distribution of the immersed boundary forcing with an efficient strategy that distributes the Lagrangian points on the surface of the immersed body is developed. We validate our method for various flows induced by a translational or angular motion of a sphere by measuring the lift, drag, and moment coefficients. For an arbitrary shape particle, we test our method for flow around an ellipsoid in the uniform flow. All tests show good agreement with available references. Finally, we investigate the interaction between a tilted ellipsoid and the wall in the uniform flow and the Poiseuille flow.