An angular weighting approach for calculating gradients and divergences
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.
KeywordsMass Point Interpolation Scheme Large Aspect Ratio Voronoi Polygon Simple Gradient
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