Abstract
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.
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For reasons of readability, we write n instead of n water and n air, respectively.
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Kuhnert, J., Michel, I., Mack, R. (2019). Fluid Structure Interaction (FSI) in the MESHFREE Finite Pointset Method (FPM): Theory and Applications. In: Griebel, M., Schweitzer, M. (eds) Meshfree Methods for Partial Differential Equations IX. IWMMPDE 2017. Lecture Notes in Computational Science and Engineering, vol 129. Springer, Cham. https://doi.org/10.1007/978-3-030-15119-5_5
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