A ghost cell method for turbulent compressible viscous flows on adaptive Cartesian grids

The aim of this paper is to present a new ghost cell turbulent wall boundary condition to simulate high Reynolds number compressible viscous flows on adaptive Cartesian grids. A pure Cartesian grid has been established with the bodies embedded into the grid. Instead of cut cell approach, a ghost cell immersed boundary method has been applied and a wall function model is devised to treat turbulent wall boundary conditions. The law-of-the-wall is employed to define primitive variables and turbulent properties at the ghost cells. Furthermore, the turbulent variables at the near wall cells and boundary cells are modified by using wall function model. In the frame of adaptive Cartesian grids, a cell-centered, second-order accurate finite volume solver has been developed for predicting turbulent flow fields. The robustness and the accuracy of the methodology have been validated versus well documented turbulent flow test problems, such as transonic flow past a RAE2822 airfoil and supersonic flow past a circle cylinder. The obtained results show the effectivity and reliability of the new numerical methods. (C) 2013 The Authors. Published by Elsevier Ltd.