Traditional BFM methods rely on the use of body-fitted grids. When the mesh is constructed, grid-generating algorithms build it around the immersed body, conforming the grid to its geometry. This method has several advantages, but the main one is that the boundary conditions on the interface between the immersed body and the fluid are very easy to implement.

However, this approach severely limits the ability to model moving objects or moving boundaries, because every time that a boundary moves, the mesh has to be reconstructed to fit the body in its new position. This can result in very expensive solutions, where mesh generating algorithms need to be used at every timestep.

On the other hand, the semi-resolved approach is based on the use of fixed grids, that do not conform to the immersed body shape, resulting in a decoupling of the positioning of the body related to grid elements, allowing it to be freely moved across the fluid domain without the need of remeshing at every timestep.

For the BFM, applying boundary conditions is quite straightforward, due to the fact that there are grid elements at the walls of the body. Thus, a non-slip condition, for example, is very easily implemented in the momentum equations. However, in the semi-resolved the process to calculate the boundary conditions is not so simple, requiring the use of a forcing function.

In the semi-resolved method, particles are treated as immersed solids that can be moved freely across the domain without the use of body-fitted meshes. A discrete forcing function is applied: the conservation equations are discretized without accounting for the presence of the body; then, the boundary conditions are implemented using the information available at the cells located near the immersed boundary. Their values are interpolated, allowing for the determination of the property at the surface of the body.