| One of the critical issues addressed very often both in research and industry is the boundary mesh generation technique for wall dominated phenomena, for example, viscous fluid flow, heat transfer, etc. This technique is called front propagation or front offset. This thesis presents a novel application of front propagation technique to domain partitioning and mesh generation processes.; The propagation process proposed in this work is directly inspired from marching technology, that is all the points located on the original front are propagated along their local normal directions. The main difference between the current method and traditional marching methods lies in the way that local normal direction is computed. Traditionally, the local normal directions are computed using geometric information, such as the average normal of neighboring points or facets surrounding the point to be propagated. In this method, the local normal directions are calculated using equation n&ar; = ∇&phis;/|∇&phis;|. Function &phis; is the numerical solution of the minimum distance equation, which is a variation of the Eikonal equation, ∇&phis; · ∇&phis; = 1.; The benefit of calculating normal directions in such a way is that self-intersections are avoided in a natural way. Since normal directions are represented using the numerical solution of the PDE, propagation is thus performed in the &phis; space rather than geometric space. In addition, the proposed method transports the original parameterization to the propagated surface, there is a one-to-one parametric consistency between the original front and its offset, which allows rigorous matching of block interfaces.; This front propagation method used was validated from two aspects: accuracy and efficiency. For accuracy, the results show that the proposed technique converges linearly with mesh size. The result follows from the fact the &phis; field is solved using a first order numerical scheme. The time spent in this propagation method is divided into three parts, and measured separately: initialization time and fast sweeping time, which both are dependent on the mesh size; propagation time, which is independent of mesh size, but dependent on the initial discretization of the front to be propagated and time increment.; The proposed front propagation technique is successfully applied in the applications of Geometric Modeling, ie, offset surface construction. The presented method can be used to offset both facet and NURBS represented geometries. When surfaces are discretized into triangular or quadrilateral surfaces, the discretization points are propagated directly and the offset points are used to construct new offset boundary; when surfaces are NURBS represented geometries, the control points are propagated using the proposed method.; Another type of application presented in this thesis is Mesh Generation, ie, boundary mesh generation. The proposed method is used to decompose the entire domain into sub-domains near boundary areas, and then hybrid meshes are generated in each sub-domain. The boundary mesh is validated using a ball valve model under both steady and unsteady flow conditions. The preliminary result shows that the presented method provides a possibility to generate boundary mesh in a robust and automated manner. |
