GPU-based Adaptive Mesh Refinement for unstructured Voronoi meshes.

In high-fidelity flow simulations, a broad shift toward GPU-accelerated computing is underway, driven by GPUs' superior performance and energy efficiency. This transition requires rethinking existing CPU-based tools and algorithms, such as adaptive mesh refinement (AMR), to enable automatic, on-the-fly, physics-driven mesh generation. Although GPU-based AMR is now well established for structured or octree grids, extending it to unstructured meshes remains a significant challenge due to irregular connectivity and load-balancing complexity. In this work, a multi-GPU implementation of AMR for unstructured Voronoi meshes is presented. The approach emphasizes algorithmic design for GPU efficiency, parallel scalability, and mesh quality preservation. The refinement regions are identified using a metric function, for instance, tracking subgrid kinetic energy or numerical truncation errors. Refinement uses Lloyd smoothing, combined with Lagrangian displacement of cell seeds to minimize a metric error functional.