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Meshfree Petrov-Galerkin Methods for the Incompressible Navier-Stokes Equations

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Meshfree Methods for Partial Differential Equations II

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 43))

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Abstract

Meshfree stabilised methods are employed and compared for the solution of the incompressible Navier-Stokes equations in Eulerian formulation. These Petrov-Galerkin methods are standard tools in the FEM context, and can be used for meshfree methods as well. However, the choice of the stabilisation parameter has to be reconsidered. We find that reliable and successful approximation with standard formulas for the stabilisation parameter can only be expected for shape functions with small supports or dilatation parameters.

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Authors and Affiliations

  1. Institute of Scientific Computing, Technical University of Braunschweig, D-38092, Braunschweig, Germany

    Thomas-Peter Fries & Hermann Georg Matthies

Authors
  1. Thomas-Peter Fries
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  2. Hermann Georg Matthies
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Editors and Affiliations

  1. Institut für Numerische Simulation, Universität Bonn, Wegelerstraße 6, 53115, Bonn, Germany

    Michael Griebel  & Marc A. Schweitzer  & 

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Fries, TP., Matthies, H.G. (2005). Meshfree Petrov-Galerkin Methods for the Incompressible Navier-Stokes Equations. In: Griebel, M., Schweitzer, M.A. (eds) Meshfree Methods for Partial Differential Equations II. Lecture Notes in Computational Science and Engineering, vol 43. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-27099-X_3

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