Geographic information systems (GISs) are widely used for representation, management, and analysis of spatial data in many disciplines. In particular, geoscientists increasingly use these tools for data integration and management purposes in many environmental applications, ranging from water resources management to the study of global warming. Beyond these capabilities, geoscientists need to model and simulate three-dimensional (3D) dynamic fields and readily integrate those results with other relevant spatial information in order to have a better understanding of the environmental problems. However, GISs are very limited for the modeling and simulation of spatial fields, which are mostly 3D and dynamic. These limitations are mainly related to the existing GIS spatial data structures that are static and limited to 2D space. In order to overcome these limitations, we develop and implement a new kinetic 3D spatial data structure based on Delaunay tetrahedralization and a 3D Voronoi diagram to support a 3D dynamic field simulation within GISs. In this article, we describe in detail the different steps from discretization of a 3D continuous field to its numerical integration, based on an event-driven method. For validation of the proposed spatial data structure itself and its potential for the simulation of a dynamic field, two case studies are presented in the article. According to our observations, during the simulation process, the data structure is maintained and the 3D spatial information is managed adequately. Furthermore, the results obtained from both experiments are very satisfactory and are comparable with the results obtained from other existing methods for the simulation of the same dynamic field. To conclude, we discuss the current challenges related to the development of the 3D kinetic data structure itself and its adaptation to 3D dynamic field simulation and suggest some solutions for its improvement.

This paper proposes a new Free-Lagrange method based on the kinetic Voronoi diagram for fluid simulation. The objective here is to combine the advantages of an adoptive mesh structure with the advantages of kinetic mesh maintenance, and demonstrate their value for dynamic simulation. Despite the theoretical advantages of the Free-Lagrange method, its use has been handicapped with the reconstruction of topology after each time step that considerably reduces the efficiency of the method. In addition, the use of fixed time steps causes problems such as overshoots and undetected collisions. In order to demonstrate the ability of the proposed model to solve these problems, the method is applied to a dam-breaking problem and global tides. With the results obtained from these numerical experiments, the validity of the global kinetic data structure is approved. In particular, the method is found to be more efficient than existing methods. In addition, qualitative comparison of physical results with analytical solutions demonstrates the similarity of the results and confirms the physical validity of the proposed method. Further investigations with real-world data and the complete equation of motion are suggested to compare it with other numerical methods.