PARTICLES 2025

MESHFREE – A Generalized Continuum Mechanics Approach for Industrial Applications

  • Sanghavi, Chaitanya (Fraunhofer ITWM)
  • Michel, Isabel (Fraunhofer ITWM)
  • Suchde, Pratik (University of Luxembourg)
  • Kuhnert, Joerg (Fraunhofer ITWM)

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Despite several advances in the field of mathematical und numerical modeling, their application to real-world industrial problems remains a challenging task. For example, the water management around a vehicle as it moves through a pool of water at realistic speeds remains a challenging problem for car manufacturers. Classical mesh-based methods face severe challenges especially for fluids or materials which undergo large deformations or have free surfaces. Moreover, meshing can be a laborious task when trying to capture physical phenomena accurately inside or around complex geometries. MESHFREE approaches offer a powerful alternative to the classical techniques. With the MESHFREE software (www.meshfree.eu), Fraunhofer ITWM develops and implements a Generalized Finite Difference Method (GFDM) using mathematical formulations for solving challenging industrial problems. The GFDM is a purely numerical approach to simulate flows or continuum mechanical processes. Due to its discretization based on a scattered set of numerical points (called point cloud), MESHFREE is very flexible and particularly efficient for applications with moving geometric parts, free surfaces, phase boundaries or fluid-structure interaction (FSI). The talk will begin by introducing the mathematical formulation and theory behind the GFDM. The second part will focus on an overview of various industrial applications where MESHFREE has been already successfully applied for industrially relevant application. The talk will conclude with a demonstration of the method’s scalability and performance across various computational aspects—such as point cloud organization, computation of differential operators, and solver efficiency—within the context of an industrially relevant application.