Contact theory

In this section, we detail different collision models based on contact and lubrication forces and allowing to model body-body or body-boundary interactions in Newtonian incompressible fluids. In particular, we consider a model introducing a repulsive force. First, we detail this model for spherical bodies moving under the effect of gravity and hydrodynamic forces, subsection Repulsive force for spherical rigid bodies. Then, we generalize it for complex shaped bodies (Repulsive force for arbitrary rigid bodies), and articulated bodies, in particular the three-sphere swimmer (Repulsive force for articulated bodies). For each kind of body, we detail the modeling, its applications and its algorithm. We realize a plug-in of the collision forces in the fluid toolbox of Feel++. In addition, we perform test cases from the literature in order to compare the results and to validate our models. In the subsection Collision model for DNS, we summarize another collision model and the subsection Implementation, gives information on the implementation and execution of the code. In the last subsection (Application), we define an algorithm to insert rigid objects of arbitrary shape into a complex meshed geometry whose CAO discretization is not available. We show some examples that allow to test this algorithm.