A second-order-accurate immersed boundary ghost-cell method with hybrid reconstruction for compressible flow simulations

Abstract

This study presents an improved ghost-cell immersed boundary method for geometrically complex boundaries in compressible flow simulations. A bilinearly complete extrapolation scheme is developed for the reconstruction of the ghost-cell. The second-order accuracy of the improved ghost-cell method (GCM) is shown in unit test cases and is also theoretically proven. A hybrid GCM based on both baseline GCM and improved GCM is proposed and constructed. The hybrid GCM applied in compressible flow is validated against five test cases: (a) Stationary rotating vortex, (b) Prandtl–Meyer expansion flow, (c) Double Mach reflection, (d) Moving-shock/obstacle interaction, (e) Blunt body shock-induced combustion. This paper provides a comprehensive comparison of their performance in terms of various accuracy and computation time measurements. The simulation results demonstrate that the hybrid GCM has higher accuracy and convergence than the remaining two GCMs in all cases. By directly comparing the primitive variables along the boundary, it can be concluded that the hybrid GCM has significant advantages in compressible flow simulations. The results of CPU time show that the hybrid GCM can provide more accurate results while ensuring the efficiency of the calculation.