Elliptic Grid Generation University of Virginia（椭圆型网格生成弗吉尼亚大学）.pdfVIP

Elliptic Grid Generation Introduction In this project you will use elliptic grid generation techniques to develop an O type grid for a two-dimensional airfoil. This exercise serves as an introduction to grid generation for odd geometries. The term “boundary-fitted coordinates” (BFC) is commonly used to describe such grids. These grids are used when the computational domain does not line up readily with a simple, e.g., Cartesian or polar, grid. In addition the project is also a somewhat advanced application of iterative methods used for solving elliptic equations. The equations to be solved are a coupled system of non-linear partial differential equations. Also one boundary condition will be taken to be periodic, rather than the fixed or derivative boundary conditions more frequently encountered with elliptic equations. The procedures discussed here are readily extended to three dimensions and to the use of Poisson rather than the Laplace equations as used here. A system of Poisson equations provides better control over interior spacing and orientation than what can be done with only Laplace equations. Background Elliptic grid generation is one of several methods used to generate structured grids for odd geometries. Algebraic methods are one commonly used alternative, and hyperbolic systems of equations are sometimes used, particularly for external flows. See, e.g., Thompson et al. (1985), Anderson et al. (1984), or Hoffman and Chiang (1993) for much more detailed information. In this project we will solve a pair of Laplace equations to generate the mesh. Rather than work in the physical domain where the geometry is complicated (which is why we are having to generate the gri