Over the last years, so-called immersed boundary methods have become increasingly popular in computational fluid dynamics. In these methods, the boundaries of obstacles in a fluid are represented on a non-conforming grid, for instance curved obstacles are represented on a Cartesian grid. The reasons for the popularity of these methods are ease of programming and cost-effectiveness. These issues are of primary importance for applications which involve costly simulations, such as LES and DNS. Moreover, these methods retain much of their elegance if additional physics complicates matter, for instance if there are moving boundaries, as in biological flows, or when many particles are added.