  In this study, an implicit scheme for the gas-kinetic scheme (GKS) on the
unstructured hybrid mesh is proposed. The Spalart-Allmaras (SA) one equation
turbulence model is incorporated into the implicit gas-kinetic scheme (IGKS) to
predict the effects of turbulence. The implicit macroscopic governing equations
are constructed and solved by the matrix-free lower-upper
symmetric-Gauss-Seidel (LU-SGS) method. To reduce the number of cells and
computational cost, the hybrid mesh is applied. A modified non-manifold hybrid
mesh data(NHMD) is used for both unstructured hybrid mesh and uniform grid.
Numerical investigations are performed on different 2D laminar and turbulent
flows. The convergence property and the computational efficiency of the present
IGKS method are investigated. Much better performance are obtained compared
with the standard explicit gas-kinetic scheme. Also, our numerical results are
found to be in good agreement with experiment data and other numerical
solutions, demonstrating the good applicability and high efficiency of the
present IGKS for the simulations of laminar and turbulent flows.
