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An angular weighting approach for calculating gradients and divergences

  • Ronald C. Kirkpatrick
Section IV: SPH and Analysis/Error Evaluation
Part of the Lecture Notes in Physics book series (LNP, volume 395)

Abstract

There are several desirable properties for a free Lagrange algorithm: 1) a Lagrangian nature, 2) reciprocity, 3) minimization of numerical noise, 4) numerical efficiency, and 5) the ability to extend the algorithms to 3-D. In addition, some integral hydro formulations allow the mass points to drift among the other points because the divergences and gradients do not depend explicitly on the position of a mass point between two other mass points. Therefore, another desirable property is G) a restoring force that keeps the mesh regular. An algorithm based on the angles subtended by the Voronoi polygon sides satisfies all the above criteria, except the fourth; this is because of the necessity of using trigonometric functions. Nevertheless, this loss of efficiency may be compensated by the avoidance of reconnection noise.

Keywords

Mass Point Interpolation Scheme Large Aspect Ratio Voronoi Polygon Simple Gradient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    H. Lass (1950) Vector and Tensor Analysis, (McGraw-Hill Book Company, Inc., New York), pp 114–120Google Scholar
  2. 2.
    H.E. Trease (1987): “Three-Dimensional Free Lagrange Hydrodynamics”, The Free-Lagrange Method, ed. M.J. Fritts, Lecture Notes in Physics 238, (Springer-Verlag, New York), pp 145–157Google Scholar
  3. 3.
    W.P. Crowley (1987) “Free-Lagrange Methods for Compressible Hydrodynamics in Two Space Dimensions”, The Free-Lagrange Method, ed. M.J. Fritts, Lecture Notes in Physics 238, (Springer-Verlag, New York), pp 1–21Google Scholar
  4. 4.
    C.D. Hodgman (1957) CRC Standard Mathematical Tables (Chemical Rubber Publishing Co., Cleveland, Ohio), pp 371–373Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Ronald C. Kirkpatrick
    • 1
  1. 1.Los Alamos National LaboratoryLos AlamosUSA

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