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A projection technique for incompressible flow in the meshless finite volume particle method

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Abstract

The finite volume particle method is a meshless discretization technique, which generalizes the classical finite volume method by using smooth, overlapping and moving test functions applied in the weak formulation of the conservation law. The method was originally developed for hyperbolic conservation laws so that the compressible Euler equations particularly apply. In the present work we analyze the discretization error and enforce consistency by a new set of geometrical quantities. Furthermore, we introduce a discrete Laplace operator for the scheme in order to extend the method to second order partial differential equations. Finally, we transfer Chorin’s projection technique to the finite volume particle method in order to obtain a meshless scheme for incompressible flow.

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Authors and Affiliations

  1. FB Mathematik, Universität Kaiserslautern, Erwin-Schrödinger-Straße, D-67663, Kaiserslautern, Germany

    R. Keck

  2. Fraunhofer-Institut für Techno- und Wirtschaftsmathematik, Gottlieb-Daimler-Straße,, D-67663, Kaiserslautern, Germany

    D. Hietel

Authors
  1. R. Keck
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  2. D. Hietel
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Correspondence to R. Keck.

Additional information

Communicated by Z. Wu and B.Y.C. Hon

AMS subject classification

65M99, 68U20, 76B99, 76M12, 76M25, 76M28

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Keck, R., Hietel, D. A projection technique for incompressible flow in the meshless finite volume particle method. Adv Comput Math 23, 143–169 (2005). https://doi.org/10.1007/s10444-004-1831-7

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  • DOI: https://doi.org/10.1007/s10444-004-1831-7

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