Abstract
A Tri-Tree Method for generating finite element grids in two and three dimensions is developed. The method is based on a new tree search structure. The search tree is built upon triangles in two dimensions and tetrahedra in three dimensions. The density of elements can be varied throughout the computational domain. A Coupled Node Fill-In ILU preconditioner for implicit and itererative solution of the Navier-Stokes equations has been designed. The properties of preconditioner, which is based on new fill-in rules, permit fill-in and preconditioning of the pressure in the equation system. The Tri-Tree grid generation algorithm includes local refinements. The spatial location of refinements are based on the solution calculated for the previous grid. The element Reynolds number is calculated for each Tri-Tree element and Tri-Tree elements with Reynolds number above a predefined limit are recursively refined. Elements with Reynolds number below this limit are recoarsed. A Prolonged Adaptive Multigrid Method, which is based on the Tri-Tree grid generation method and the Coupled Node Fill-In preconditioner is developed. The Prolonged Adaptive Multigrid Method reveals advantages in both robustness and efficiency, especially for nonlinear and nonpositive definite equation systems. In order to reduce the overall work, the element matrices are integrated analytically.
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