Research On The Numerical Method Of Space-time Conservation Element And Solution Element

The Space-Time Conservation Element and Solution Element (CE/SE) method is studied in this paper. It is a new numerical framework for solving the conservation laws. On the base, the CE/SE program is developed to solve the Euler and Navier-Stokes equations from 2-D to 3-D, and subsonic, transonic, supersonic flow and low speed incompressible flow are computed.Firstly, the a-μand a-εschemes are introduced. Then, we construct the conservation element and solution element of triangle grid. The computation of the conservation variables and the space derivatives, the treatment of viscous term and the treatment of boundary conditions are introduced in the following. The FORTRAN program is developed based on the CE/SE method. The oblique shock problem and front step problem are used to validate the program. Secondly, the simulations of a driven cavity (Re=400) and a shock/boundary interaction problem are carried out. It means that the method can calculate flows at wide speed range. The 3-D unstructured Euler and Navier-Stokes Solvers are introduced in the following. The 3-D simulations of oblique shock problem and a driven cavity (Re=400) are also carried out in this thesis.Finally, we develop the traditional CE/SE method so that it can also run on dynamic meshes. The flow past a pitching airfoil harmonically about the quarter chord is simulated, and the numerical results obtained are in good agreement with available experimental data.