Robust and Efficient Cartesian Mesh Generation for Component-Based Geometry

TLDR

This work documents a new method for rapid and robust Cartesian mesh generation for component‑based geometry. The algorithm first intersects components to extract the wetted surface using a robust geometry engine with adaptive precision arithmetic and tie‑breaking for degeneracies, then generates a volume mesh by dividing an initially uniform coarse grid based on the surface triangulation, refining hexagonal cells while preserving directional alignment with local geometry. The intersection procedure runs in O(N log N) time and scales to 121 overlapping components, while the mesh generation achieves linear asymptotic complexity, uses only 14–17 words per cell, and reaches about 10⁶ cells per minute on a typical workstation.

Abstract

This work documents a new method for rapid and robust Cartesian mesh generation for component-based geometry. The new algorithm adopts a novel strategy that first intersects the components to extract the wetted surface before proceeding with volume mesh generation in a second phase. The intersection scheme is based on a robust geometry engine that uses adaptive precision arithmetic and automatically and consistently handles geometric degenerades with an algorithmic tie-breaking routine. The intersection procedure has worst-case computational complexity of O(N log N) and is demonstrated on test cases with up to 121 overlapping and intersecting components, including a variety of geometric degeneracies. The volume mesh generation takes the intersected surface triangulation as input and generates the mesh through cell division of an initially uniform coarse grid. In refining hexagonal cells to resolve the geometry, the new approach preserves the ability to directionally divide cells that are well aligned with local geometry. The mesh generation scheme has linear asymptotic complexity with memory requirements that total approximately 14-17 words/cell. The mesh generation speed is approximately 10 6 cells/minute on a typical engineering workstation