Efficient adaptive Cartesian mesh generation for complex boundary representation models

Abstract

Cartesian mesh-based fluid simulation methods are gaining popularity due to their fully automated mesh generation capabilities for geometries without repair. The performance and flexibility of Cartesian mesh generation significantly influence their application across various fields. This study introduces an efficient adaptive Cartesian mesh generation framework directly for arbitrary geometries. Initially, we propose a robust, high-quality build-in tessellation method and compute proximity. Subsequently, we design a hierarchical storage method combined with binary search for efficient intersection determination. To enhance flexibility, a fully unstructured data type and compressed data representation are established. Finally, we develop a four-step refinement mechanism to achieve geometric adaptation and smooth transitions effectively. The robustness and efficiency of the approach were validated through typical case studies, demonstrating that the mesh generation process for complex models can reach speeds of up to $10^5$ cells per second, which presents significant potential to address the challenges of real-time simulations.