A p-multigrid compact gas-kinetic scheme for steady-state acceleration

In this paper, the high-order compact gas-kinetic scheme (CGKS) on three-dimensional hybrid unstructured mesh is further developed with the p-multigrid technique for steady-state solution acceleration. The pmultigrid strategy is a two-level algorithm. On the high-order level, the CGKS with high-order compact initial reconstruction is used to evolve both cell-averaged conservative flow variables and their gradients at the beginning of next time step. On the low-order level, starting from the high-order level solution the cell-averaged conservative flow variables is evolved by a first-order scheme, where implicit backward Euler smoother is adopted for accelerating the convergence of steady-state solution. The final iterative updating scheme becomes numerically simple and computationally efficient. The effectiveness of the p-multigrid method is validated in both subsonic and supersonic flow simulations in two-and three-dimensional space with hybrid unstructured mesh. One order of magnitude speedup in the convergence rate has been achieved by the approach in comparison with the explicit counterpart.