Grid-Free Methods

In contrast to classical numerical methods such as finite elements or finite volumes, meshfree methods do not require a grid and thus no - sometimes very time-consuming - meshing of the flow domain. We develop a general continuum mechanical approach based on a Generalized Finite Difference Method (GFDM), also known as Finite Pointset Method (FPM). In addition to common fluid dynamic processes, this approach can model a wide variety of nonlinear physical phenomena such as non-Newtonian fluids and other complex materials.

The fluid dynamic properties (e.g. velocity, pressure, temperature) are stored on freely positionable information carriers (the so-called point cloud), which are moved with the flow in case of time-dependent problems. Therefore, this approach is perfectly suited for all problems where mesh-based methods reach their limits due to the necessary remeshing.
 

Examples are:

• fluid dynamical problems with free surfaces
• multiphase flows
• fluid-structure-interactions (FSI) with strong changes in the computational domain
  
• structural mechanical problems with substantial structural changes
  

Meanwhile, this approach exists in a compressible and an incompressible variant, each of which can be extended modularly. Furthermore, a separate discrete element solver is integrated, which can be coupled with the incompressible solver, for example.