Three-dimensional Free-Lagrange hydrodynamics

Abstract This paper presents a description of a three-dimensional Free-Lagrange code. The Free-Lagrange Method (FLM) is characterized by a global connectivity matrix that describes the “nearest” neighbor connections between the Lagrangian mass points. The nearest neighbor connectivity is dynamic with respect to time, so it must be constructed at time equal 0.0 and maintained thereafter. The code described in this paper explicitly integrates the 3-D fluid equations in time and space. Spatial derivatives are derived from area and volume weighted averages of quantities over the set of “nearest” neighbors for each point. The global connectivity matrix is maintained (and constructed) with a Voronoi mesh construction algorithm, where each pair of nearest neighbors are separated by a perpendicular bisecting plane. The spatial integration algorithm uses the Voronoi polyhedron as the integration control volume, but as discussed the median polyhedron will be used as the integration control volume in the future.