Voronoi mesh generation tailored for urban flow simulations
Ákos Sárkány (TU Delft - Architecture and the Built Environment)
C. Garcia Sanchez – Mentor (TU Delft - Urban Data Science)
H. Ledoux – Mentor (TU Delft - Urban Data Science)
A. Patil – Mentor (TU Delft - Urban Data Science)
F.R. Schnater – Graduation committee member (TU Delft - Building Design & Technology)
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Abstract
Accurate urban Computational Fluid Dynamics (CFD) simulations require volumetric meshes whose boundary conforms to complex city geometry while maintaining cell quality and enabling adaptive mesh sizing. This thesis develops a Voronoi-based polyhedral meshing methodology tailored to the output of City4CFD, where the simulation domain is provided as a triangulated Piecewise Linear Complex (PLC) whose faces are grouped into semantic boundary patch types. The central goal is to generate a boundary-conforming polyhedral mesh without clipping Voronoi cells against the boundary, and to preserve patch information so that CFD boundary conditions can be transferred consistently to the mesh.
The method constructs a set of boundary (surface) Voronoi sites by intersecting triplets of spheres centered at the vertices of a refined surface triangulation. Building on the sphere-based sampling conditions of VoroCrust, sphere radii are initialized and iteratively adjusted to satisfy smooth-coverage, smooth-overlap, and Lipschitz-type size-transition constraints, while a shrinking step resolves "half-covered" seed configurations. The surface triangulation is refined by splitting triangles and protecting edges, then regularized with centroidal smoothing until the triangles associated with each facet intersect in two points, yielding paired sites on opposite sides of the boundary. These sites induce Voronoi facets that coincide with the input surface, producing triangular boundary faces and avoiding cell clipping. Patch-boundary preservation is enforced by identifying protected edges not only via dihedral-angle sharpness but also via changes in patch groups, ensuring that 1D interfaces between patch types are explicitly represented in the resulting Voronoi boundary.
To populate the mesh interior with Voronoi sites, the thesis evaluates several strategies (uniform random scattering, adaptive distance-based refinement, and structured lattices) to regulate cell density and promote larger cells away from geometric features. A prototype implementation in C++ using CGAL demonstrates feasibility for 2-manifold inputs and produces boundary-conforming Voronoi meshes compatible with OpenFOAM-style polyhedral representations. The approach assumes a valid 2-manifold boundary and does not repair non-manifold or overlapping input geometries.