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

An Implicit Gas-Kinetic Scheme for Turbulent Flow on Unstructured Hybrid Mesh