In this talk, I will present some researches on adaptive Cartesian grid methods for compressible flow. At first, I will introduce the adaptive Cartesian grid method with ghost cell immersed boundary method. Second, an h-adaptive Cartesian grid RKDG method will be presented to simulate inviscid compressible flow with complex geometry, and a positivity-preserving RKDG method on adaptive Cartesian grid for strong moving shock over complex geometry will also be introduced. In order to simulate the high Reynolds number viscous compressible flow on Cartesian grid, a special ghost cell immersed boundary method with wall function is shown. At last, an adaptive Cartesian grid method with hybrid body-fitted grid for compressible viscous flow will be given.
 

Dr. Jianming Liu now is an Associate Professor and the Department Head of Computational Science, School of Mathematics and Statistics, Jiangsu Normal University. Dr. Liu obtained his PhD degree in the subject of fluid dynamics from Nanjing University of Aeronautics and Astronautics in 2010, and also achieved a PhD degree in the subject of mechanical engineering from De Montfort University Leicester in England. His main research interests included the immersed boundary method, adaptive Cartesian grid method and the numerical method for partial differential equations. He has finished a project supported by National Natural Science Foundation of China, and is also a main member in several projects supported by National Natural Science Foundations of China.