The study on adaptive Cartesian grid methods for compressible flow and their applications
This research is mainly focused on the development of the adaptive Cartesian grid methods for compressibl e flow. At first, the ghost cell method and its applications for inviscid compressible flow on adaptive tree Cartesian grid are developed. The proposed method is successfully used to evaluate various inviscid compressible flows around complex bodies. The mass conservation of the method is also studied by numerical analysis. The extension to three-dimensional flow is presented. Then, an h-adaptive Runge–Kutta discontinuous Galerkin (RKDG) method is presented in detail for the development of high accuracy numerical method under Cartesian grid. This method combined with the ghost cell immersed boundary method is also validated by well documented test problems involving both steady and unsteady compressible flows over complex bodies in a wide range of Mach numbers. In addition, in order to suppress the failure of preserving positivity of density or pressure, which may cause blow-ups of the high order numerical algorithms, a positivity-preserving limiter technique coupled with h-adaptive RKDG method is developed. Such a method has been successfully implemented to study flows with the large Mach number, strong shock/obstacle interactions and shock diffraction. The extension of the method to viscous flow under the adaptive Cartesian grid with hybrid overlapping bodyfitted grid is developed. The method is validated by benchmark problems and has been successfully implemented to study airfoil with ice accretion. Finally, based on an open source code, the detached eddy simulation (DES) is developed for massive separation flow, and it is used to perform the research on aerodynamic performance analysis over the wing with ice accretion.
- PhD