A p-multigrid compact gas-kinetic scheme for steady-state acceleration. (15th June 2022)

• Record Type: Journal Article
• Authors: Ji, Xing; Shyy, Wei; Xu, Kun
• Is Part Of: Computers & fluids. Volume 241(2022)
• Publication Date: 2022-06-15
• Subjects: Compact gas-kinetic scheme -- p-multigrid -- Navier–Stokes solution -- Hybrid mesh; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2022.105489
• Languages: English
• ISSNs: 0045-7930

Abstract

Abstract: 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 p-multigrid 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. Highlights: The p-multigrid technique is firstly adopted to the compact gas-kinetic scheme. One order of magnitude speedup is achieved compared with the explicit counterpart. The resulting two-level p-multigrid compact gas-kinetic scheme is simple and robust. The effectiveness of the proposed method is validated in 2-D and 3-D flow simulations.