Development Of Cartesian Grid Method Forcomplex Compressible Flows And Its Applications

Due to possessing flexibility in grid generation and ability of adaptive mesh refinement(AMR), Cartesian grid method has been widely used for the simulation of flows with complex geometries or complicated characteristics. Nowadays, main challenge to the Cartesian gird method is how to implement boundary conditions for compressible flows. Generally, the available Cartesian grid methods for treating compressible flow boundary condition can be divided into two categories: “body-fitted” type and “non-body-fitted” type. These methods still require to be further developed. Therefore, in this work, some efficient Cartesian grid boundary methods are developed to simulate complex compressible flows. Roughly, the current research work includes following three aspects: AMR technique based Cartesian grid generation method, Cartesian grid boundary treatment methods, and numerical validation of developed Cartesian grid methods.The content of thesis has the following parts:1) Study about combination of Cartesian grid generation method and adaptive mesh refinement technique. The obtained method can deal with complex geometries. Meanwhile, it also can perform the dynamic adaptive grid refinement according to the flow features. The list data structure, mesh refinement criterion, gradient calculation under Cartesian grid, and the treatment of the “new born” cells have been investigated. Furthermore, a new Open MP type parallel computing technique based on list data structure is presented to improve the computational efficiency.2) Study about "body-fitted" type Cartesian grid boundary treatment method. Based on the idea of hybrid grid, an adaptive hybrid Cartesian grid(AHCG) method is developed. A “donor cell” method is given to treat the interface region between the body-fitted mesh and Cartesian mesh, in which an ADT “donor cell” search method is investigated. Furthermore, there are three typical unsteady vortex dominated flow(VDF) problems, including the unsteady wake flows, airfoil-vortex interaction, and turbulent separation flows, in the aerodynamic interference of helicopter. In order to simulate these problems and analyze the underlying physical mechanisms, an unsteady AHCG method is further developed. The established numerical results indicate that the proposed method has convincing efficiency and accuracy.3) Study about “non-body-fitted” Cartesian grid boundary treatment method. Based on the idea of immersed boundary method, a new ghost cell method is developed. Firstly, considering the curved geometry, an improved ghost cell method is presented, which named as normal correction ghost cell method. Furthermore, a new wall function-ghost cell method is developed for high Reynolds number compressible flows. Based on the basic assumptions of wall function model and the ghost cell method, this method defines the virtual flow information on ghost cells and the turbulent wall boundary conditions on “non-body-conforming” Cartesian grids. On this basis, coupling with flowfield numerical method, a novel Cartesian grid ghost cell method is developed for simulation of compressible flows.