9500394 Patrikalakis The objective of this project is to construct numerically robust and topologically reliable unstructured triangular meshes of surfaces which are the faces of complex solid models for computational fluid dynamics. The project builds on fundamental work completed earlier by these investigators in interval solid modeling to address basic robustness problems in interrogation methods for solid models. The research plan involves first the conversion of older legacy designs to interval solid models to maximize impact of the method in large-scale industrial rather than only academic problems. The research will also explore some of the essential elements of piecewise linear and topologically reliable approximation of planar contours, followed by three dimensional contours that can represent space interval non-uniform rational B-spline curves of arbitrary complexity. This will be extended to explore features of surface triangularization of surface patches and entire solids, followed by three dimensional domain tetrahedrization. This sequence of problems, where the solution of an earlier problem assists in the solution of a more complex problem, is expected to allow the development of a reliable and efficient overall algorithm for solving such problems. An industrial advisory committee will follow the work and assure its relevance to long-term industrial interests. This work seeks to advance the state of knowledge in robustly interrogating the geometry of complex objects using imprecise or discrete computer arithmetic and developing the necessary theory and relevant algorithms which can form the intellectual basis for computer-aided design and computer-aided manufacturing (CAD/CAM) systems of the future. It could significantly decrease the time required during product design and hence decrease production cost. It could also decrease the rate of failure of design processes. It provides a sound and flexible basis for future CAD/CAM systems because these will need to includ e precise simulation of kinematics, fluid, structural and dynamical process on complex objects during the design, manufacturing and operational period of the object. The knowledge and experience gained through this research will be integrated into the teaching curriculum of two graduate courses at MIT.
