Convergence acceleration for subiterative DDADI/D3ADI using multiblock implicit boundary condition

Abstract

Developing accurate, robust and efficient implicit time-marching method is crucial for the rapid convergence of high Reynolds number wall-bounded flows. In the presence that a massive structured grid is partitioned into multiple multiblocks for parallelization, a real-time implicit boundary condition treatment taking the multiblock communications into account affects the convergence acceleration dramatically. In this paper, an implicit boundary condition (IBC) incorporated with the subiteration technique is proposed for DDADI and diagonalized DDADI (D3ADI) time-integration schemes to speed up their convergence rates. The compressible Reynolds-averaged Navier-Stokes (N–S) equations along with the Spalart-Allmaras (S–A) turbulence model can be advanced robustly in time with large admissible Courant–Friedrichs–Lewy (CFL) numbers. The accelerated efficiency stems from two reasons: (1) the subiteration technique is beneficial to eliminate the errors arising from the approximation factorization decomposition process; (2) the IBC technique is advantageous to remove the error accumulated at multiblock interfaces. The combination of these two techniques results in the fact that the implicit matrix equations are solved in an intact implicit manner no matter how many multiblock interfaces are involved. Four numerical cases are investigated where detailed comparisons of convergence acceleration are presented. The advantage of implicit boundary condition (IBC) over explicit boundary condition (EBC) is way more prominent. Meanwhile, the importance of keeping the implicit treatment of turbulence model to be consistent with N–S equations is also put forward, otherwise the convergence characteristics of N–S equations will be adversely affected. Lastly, with increasingly partitioned multiblocks, the subiterative DDADI/D3ADI with IBC still preserves good convergence behavior whereas those with EBC are likely to suffer from divergence.