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A Meshfree Method for the Analysis of Planar Flows of Inviscid Fluids

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Meshfree Methods for Partial Differential Equations VI

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 89))

Abstract

A variant of a vortex particle-in-cell method is proposed for computing 2D inviscid incompressible flows in a closed domain. The governing equations are the 2D Euler equations in terms of the stream function and the vorticity, or geophysical models of the atmosphere. The approach is based on an approximation of the vorticity field using its values at a set of fluid particles and the stream function is computed by a Galerkin method. The flow domain is divided into rectangular cells. Vorticity in every cell is interpolated by a third order polynomial. The resultant piecewise continuous polynomial approximation of the vorticity is employed to derive analytically Galerkin’s coefficients of the stream function expansion. A parallel algorithm of the proposed method is also presented. The performance of the method is illustrated by some numerical results dealing with flows trough channels and the dynamics of the multipoles vortex patch calculation.

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Acknowledgements

The author would like to acknowledge the grants 11-01-00708 and 12-01-00668 from the Russian Foundation for Basic Research.

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Authors and Affiliations

  1. Southern Federal University, Milchakova str. 8a, Rostov-on-Don, Russia

    Vasily N. Govorukhin

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  1. Vasily N. Govorukhin
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Correspondence to Vasily N. Govorukhin .

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Editors and Affiliations

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

    Michael Griebel

  2. Institut für Parallele, und Verteilte Systeme, Universität Stuttgart, Universitätsstraße 38, Stuttgart, 70569, Germany

    Marc Alexander Schweitzer

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Govorukhin, V.N. (2013). A Meshfree Method for the Analysis of Planar Flows of Inviscid Fluids. In: Griebel, M., Schweitzer, M. (eds) Meshfree Methods for Partial Differential Equations VI. Lecture Notes in Computational Science and Engineering, vol 89. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32979-1_11

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