Implicit gas-kinetic BGK scheme with multigrid for 3D stationary transonic high-Reynolds number flows

Instead of solving the Euler and Navier–Stokes equations directly, the gas-kinetic BGK scheme based on the Boltzmann equation has been developed and attracted more and more attentions since the early 1990s. It shows high accuracy and robustness for a wide range of flow regimes. But an obvious disadvantage of the BGK scheme is the low computational efficiency, in particular for multidimensional problems. Till now it has not been widely used as a practical tool for science and engineering applications. To overcome this drawback, in this paper some acceleration techniques, including local time stepping, implicit LU-SGS method, and multigrid strategy, are implemented into the original BGK approach and the new scheme is applied to study 3D steady transonic viscous flows. Numerical results show the significant speed up of the scheme to capture the steady state solution.

► Develop an implicit BGK scheme with multigrid for steady viscous flows.
► Local time-stepping, LU-SGS method and multigrid have been used.
► Convergence is accelerated significantly by adopting techniques listed above.
► The improved scheme has been shown to give excellent solutions.