A Domain-Free Discretization Method And It's Applications

This dissertation presents the local domain-free discretization (DFD) method for the solution of Navier-Stokes/Euler equations in conservative form. For DFD, the discretization strategy is that for any complex geometry, there is no need to introduce coordinate transformation and the discrete form of governing equations at an interior point may involve some points outside the solution domain. The functional values at the exterior dependent points are updated at each time step to impose the wall boundary condition by the approximate form of solution in the normal direction to the wall boundary. Some points inside the solution domain are constructed for the approximate form of solution, and the flow variables at the constructed points are evaluated by linear interpolation over triangles. The numerical schemes used in DFD are the finite element Galerkin method for spatial discretization and the dual-time scheme for temporal discretization.A Level-Set method is also developed to track the body surface efficiently in the application of the DFD method for moving-body problems.At last, a series of numerical experiments of compressible and incompressible flows over fixed and moving bodies are presented, which demonstrate the method's reliability.