Finite Pointset Method (FPM): Meshfree flow solver with applications to viscous jets and droplet dynamics
J. Kuhnert (Fraunhofer ITWM, Germany)
FPM is a young CFD tool, developed in the Fraunhofer Institute for Industrial Mathematics, Kaiserslautern. It is a meshfree approach, mainly designed to overcome several drawbacks of classical CFD methods. FPM evolved originally from classical SPH, however it developed towards a general finite difference scheme operating on non-structured point clouds. It is a Lagrangian idea, i.e. the point cloud moves with local fluid velocity. Each point carries relevant information and has to be integrated in time.
We model the incompressible Navier-Stokes equations. Here we employ Chorin's projection idea in order to maintain the incompressible character of the flow. An extension of this idea even leads to more freedom, such that compressible flows can be computed as well. The integration method is implicit in time. That relaxes the CFL-condition (i.e. upper bound for the time step size), however it requires the construction and solution of big, sparse linear systems of equations.
The biggest advantage of FPM is its easy handling of free surfaces and multiphase flows. No additional algorithms have to be employed in order to model free surfaces, as the point cloud itself describes the topology of the free boundaries. The points belonging to a free surface or an interface have to be detected and maintained at each time step.
Another advantage of FPM is its easy handling of flow problems with moving boundaries and complicated geometries. The point cloud perfectly organizes itself through the point movement.
Due to its technical and numerical character, FPM is a favoured technique for the simulation of the behaviour of viscous jets, droplets, etc. They all have in common that they are governed by free surface boundaries in conjunction with surface tension. In the presentation, some of these numerical examples will be demonstrated.