  In this paper, we present an advanced high-order compact gas-kinetic scheme
(CGKS) for 3D unstructured mixed-element meshes, augmented with a geometric
multigrid technique to accelerate steady-state convergence. The scheme evolves
cell-averaged flow variables and their gradients on the original mesh. Mesh
coarsening employs a two-step parallel agglomeration algorithm using a random
hash for cell interface selection and a geometric skewness metric for deletion
confirmation, ensuring both efficiency and robustness. For the coarser meshes,
first-order kinetic flux vector splitting (KFVS) schemes with explicit or
implicit time-stepping are used. The proposed multigrid CGKS is tested across
various flow regimes on hybrid unstructured meshes, demonstrating significant
improvements. A three-layer V-cycle multigrid strategy, coupled with an
explicit forward Euler method on coarser levels, results in a convergence rate
up to ten times faster than standard CGKS. In contrast, the implicit
lower-upper symmetric Gauss-Seidel (LU-SGS) method offers limited convergence
acceleration. Our findings indicate that the explicit multigrid CGKS is highly
scalable and effective for large-scale computations, marking a substantial step
forward in computational fluid dynamics.
