An angular weighting approach for calculating gradients and divergences

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.