Fluid Structure Interaction (FSI) in the MESHFREE Finite Pointset Method (FPM): Theory and Applications

  • Jörg KuhnertEmail author
  • Isabel Michel
  • Reiner Mack
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 129)


Fluid Structure Interaction (FSI) and meshfree numerical methods are a perfect couple. One often repeated strong argument is the almost natural coupling of meshfree methods in a Lagrangian/ALE formulation with moving, flexible structures.

Since 1996, Fraunhofer ITWM has been developing a Generalized Finite Difference Method (GFDM), a purely meshfree solver for fluid and continuum mechanics. In the industrial context, this method is also referred to as Finite Pointset Method (FPM). Currently, it is further developed to an integrated tool called MESHFREE which combines the advantages of GFDM/FPM as well as SAMG, a fast solver for large sparse linear systems developed by Fraunhofer SCAI. This synergy drastically increases the applicability of the method since SAMG provides a robust and scalable linear solver for a wide class of problems.

In this contribution, we classify fundamental FSI aspects in GFDM/FPM: classical pressure–velocity coupling and alternative velocity–pressure coupling. Each category will be illustrated by industrially relevant examples, with special focus on Pelton turbine applications and flow in flexible tubes.


  1. 1.
    A. Jefferies, J. Kuhnert, L. Aschenbrenner, U. Giffhorn, Finite pointset method for the simulation of a vehicle travelling through a body of water, in Meshfree Methods for Partial Differential Equations VII, ed. by M. Griebel, M. Schweitzer. Lecture Notes in Computational Science and Engineering, vol. 100 (Springer, Cham, 2015)Google Scholar
  2. 2.
    J. Kuhnert, Finite pointset method (FPM): meshfree flow solver with applications to elasto-plastic material laws, in Proceedings First International Conference on Particle-Based Methods, PARTICLES 2009, ed. by E. Oñate, D.R.J. Owen (CIMNE, Barcelona, 2009), pp. 423–426Google Scholar
  3. 3.
    J. Kuhnert, Meshfree numerical schemes for time dependent problems in fluid and continuum mechanics, in Advances in PDE Modeling and Computation, ed. by S. Sundar (Ane Books, New Delhi, 2014)Google Scholar
  4. 4.
    I. Michel, S.M.I. Bathaeian, J. Kuhnert, D. Kolymbas, C.-H. Chen, I. Polymerou, C. Vrettos, A. Becker, Meshfree generalized finite difference methods in soil mechanics. Part II: numerical results. Int. J. Geosci. 8(2), 191–217 (2017)zbMATHGoogle Scholar
  5. 5.
    I. Ostermann, J. Kuhnert, D. Kolymbas, C.-H. Chen, I. Polymerou, V. Smilauer, C. Vrettos, D. Chen, Meshfree generalized finite difference methods in soil mechanics. Part I: theory. Int. J. Geosci. 4(2), 167–184 (2013)MathSciNetzbMATHGoogle Scholar
  6. 6.
    S. Schröder, I. Michel, T. Seidel, C.M. König, STRING 3: full 3D visualization of groundwater flow, in Proceedings of IAMG 2015—17th Annual Conference of the International Association for Mathematical Geosciences, ed. by H. Schaeben, R. Tolosana Delgado, K.G. van den Boogaart, R. van den Boogaart (2015), pp. 813–822Google Scholar
  7. 7.
    T. Seidel, C. König, M. Schäfer, I. Ostermann, T. Biedert, D. Hietel, Intuitive visualization of transient groundwater flow. Comput. Geosci. 67, 173–179 (2014)CrossRefGoogle Scholar
  8. 8.
    T. Seifarth, Numerische Algorithmen für Gitterfreie Methoden zur Lösung von Transportproblemen, PhD thesis, Universität Kassel, 2018Google Scholar
  9. 9.
    A. Tramecon, J. Kuhnert, Simulation of Advanced Folded Airbags with VPS PAMCRASH/FPM: Development and Validation of Turbulent Flow Numerical Simulation Techniques Applied to Curtain Bag Deployments, SAE Technical Paper 2013-01-1158 (2013)Google Scholar
  10. 10.
    E. Uhlmann, R. Gerstenberger, J. Kuhnert, Cutting simulation with the meshfree finite pointset method. Proc. CIRP 8(Suppl. C), 391–396 (2013). 14th CIRP Conference on Modeling of Machining Operations (CIRP CMMO)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Fraunhofer Institute for Industrial Mathematics ITWMKaiserslauternGermany
  2. 2.Voith Hydro Holding GmbH & Co. KGHeidenheimGermany

Personalised recommendations