Geometry and mesh generation for high fidelity computational simulations using non-uniform rational B-splines

High fidelity simulations using mesh-based computational technologies such as computational fluid dynamics and computational structural mechanics are very important in providing valuable performance information of a design. These simulations, however, require accurate geometry representation as well as high quality meshes about the design in order to obtain accurate data. Unfortunately, while three-dimensional complex geometry is involved, it is a challenge to maintain geometry fidelity while trying to obtain high quality meshes. This paper discusses detailed information associated with non-uniform rational B-splines (NURBS) and its utilizations for geometry and mesh generation. It will go beyond regular curve and surface formulations to include NURBS volume and dynamic NURBS. Detailed NURBS formulations are described through mathematical expressions and applications to demonstrate the versatility and reliability of NURBS in geometry and mesh generation that enable high performance computational simulations.