Pm - Empty Conserved Jie Yuan Method Values

The Space-Time Conservation Element and Solution Element (CE/SE) method is a new numerical method for the conservation laws. In this thesis, the CE/SE method is studied. On the bases, the CE/SE program using unstructured grid is developed to solve the Euler and Navier-Stokes equations, and the subsonic, transonic, supersonic flow and low speed incompressible flow are computed.Firstly, the CE/SE numerical methods are introduced, including the construction of conservation elements (CE) and solution elements (SE), the computation of the conservation variables and the space derivatives, the treatment of the viscous terms and the treatment of the boundary conditions. Based on the above method, the FORTRAN program is completed. The subsonic shear flow and the front step flow are used to validate the program.Secondly, in this thesis, simulations of a driven cavity flow, a shock/boundary layer interaction problem and flow over cylinders are carried out. The present approach can calculate flows at wide speed range.Finally, the parallel program based on the CE/SE method has been investigated. The improved CE/SE method and a suitable parallel domain decomposition strategy has been used to develop the parallel program for solving the Euler equations, based on the unstructured grid. Some standard test cases that contained NACA0012 airfoil in subsonic and transonic flow and multi-element airfoil in low speed flow are computed. Compared with experimental data, the effectiveness and reliability of the method are verified by numerical results. At the same time, the parallel domain decomposition method here can achieve load balance between computing processors, and save computational time effectively.