Finite volume droplet trajectories for icing simulation

During a Lagrangian icing simulation, it is necessary to calculate a large number of droplet trajectories to determine the water catch, and as a result it is important that this procedure is as rapid as possible. In order to arrive at a method with minimum complexity, a finite volume representation of streamlines is extended to incorporate the equations of motion for a droplet. Using a finite volume representation means that the accuracy of the droplet motion is consistent with the underlying flow simulation, and that any flow cell may be crossed in a single timestep as the velocity is constant and the trajectory is therefore a sequence of straight line segments. However, since cells vary greatly in size, the method must be implicit to avoid a stability restriction which would otherwise degrade performance. Therefore, an implicit method is implemented by carrying out a handful of coupling iterations for every cell for each timestep, so that the droplet motion is tightly coupled to the underlying flow. By crossing every cell in a single step, and by using the mesh connectivity to track the droplet motion between cells, any need for costly searches is eliminated and the resulting method is very efficient. The final method is able to find 100000 trajectories on a mesh of 460000 cells in only 2-3 minutes, using standard hardware and unoptimised code and carrying an I/O overhead.