Cartesian grid method for moderate-reynolds-number flows around complex moving objects

A method is presented to simulate the fluid dynamics of low- to moderate-Reynolds-number flows around solid objects with complex shapes on a fixed Cartesian grid. On grid points occupied by a solid object, the method forces the fluid motion to be equal to the motion of the solid object, whereas the boundary conditions on the solid-fluid interface are enforced through a specific treatment of grid points close to the interface. The method is fairly easily implemented in both two and three dimensions, and a grid-refinement study shows that the method is globally close to second-order accurate. Steady and unsteady flow results over a cylinder and a sphere fixed in the grid show very good agreement with previous experimental and computational investigations. Computations of a cylinder moving in the grid with a surrounding fluid initially at rest produce results that compare very well with the fixed-cylinder results, thus demonstrating the validity of the method for moving geometry simulations. The method's applicability to investigations of the unsteady aerodynamics of microscale flapping flight is demonstrated through simulations of the fluid dynamics of a flapping cantilever beam and a free-failing two-dimensional "leaf".