A LAGUERRE VORONOI BASED SCHEME FOR MESHING PARTICLE SYSTEMS

Area of Science:

• Computational geometry
• Scientific computing
• Meshing algorithms

Background:

• Particle systems are fundamental in simulating physical phenomena.
• Generating high-quality conformal meshes for particle systems is computationally challenging.
• Existing methods often struggle with complex particle geometries and dynamic changes.

Purpose of the Study:

• To develop novel Laguerre Voronoi based subdivision algorithms for quadrilateral and hexahedral meshing.
• To create particle-conforming, smooth, and differentiable meshes for 2D and 3D particle systems.
• To extend the algorithms for dynamic re-meshing scenarios.

Main Methods:

• Utilizing Laguerre Voronoi diagrams to partition bounded regions containing particles.
• Decomposing Voronoi cells into initial quadrilateral/hexahedral scaffolds.
• Applying recursive subdivision techniques with specific averaging rules for mesh refinement.

Main Results:

• Generation of particle-conforming quadrilateral and hexahedral meshes.
• Meshes exhibit good quality, smoothness, and differentiability.
• Demonstrated extensions for dynamic re-meshing (particle addition, deletion, movement).

Conclusions:

• The proposed Laguerre Voronoi based subdivision algorithms provide an effective approach for meshing particle systems.
• The resulting meshes are suitable for applications in composite materials, molecular dynamics, and astrophysics.
• The dynamic re-meshing capabilities enhance the algorithms' utility in evolving simulations.