Dynamic-mesh finite element method for Lagrangian computational fluid dynamics
Finite Elements in Analysis and Design - Robert J. Melosh medal competition
Star splaying: an algorithm for repairing delaunay triangulations and convex hulls
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics)
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This paper proposes a 3D Free-Lagrange algorithm for the numerical simulation of three dimensional groundwater flow and mass transport problems. The algorithm is particularly efficient for free-surface tracking, which is applicable to water table aquifers. The proposed method is based on 3D kinetic Voronoi and Delaunay data structures and can generate a mesh that accurately represents the geometry and the characteristics of 3D hydrogeological systems. This mesh is dynamic and can be interactively improved using topological-dynamic operations. Users can thus modify and adjust the density of the mesh elements locally and on-the-fly, for example by refining the mesh in areas with higher fluxes or concentration gradients, or reducing the element density in regions where fluxes and gradients are smaller. During a fluid flow simulation, the mesh moves and the topology, connectivity, and physical parameters (e.g. hydraulic conductivity, porosity, velocity and mass) of the mesh cells are updated at each time step. In addition, to solve the problems resulting from using a fixed time step, such as overshoots and undetected collisions, an event-driven algorithm has been designed to detect events by 3D Delaunay data structure.