We are building a prototype to perform moving mesh simulations in the Lagrangian framework. Our meshes are built of Bezier triangles and object boundaries are represented in terms of B-spline curves. As the mesh moves we keep track of object boundaries, and modify it to keep it well shaped by applying the operations of edge flipping, vertex insertion and deletion, and curve smoothing. We discuss a calculus of geometric primitives for Bezier curves and triangles that we employ to implement the above operations. In addition we discuss the organization and key components of our prototype, and present experimental results.
Our target application is Navier-Stokes blood flow simulations in three dimensions, here we focus first on two-dimensional simulations, utilizing many procedures which generalize well to higher dimension applications. The system is designed for any fixed-order Bezier elements and B-Splines. In this work we have concentrated on quadratics, although most of the operations are valid for any order elements. The current simulations are based on convection equations rather than Navier-Stokes for simplicity.
This material is based upon work supported by National Science
Foundation under Grant No. 0122581.
Any opinions, findings, and conclusions or recommendations expressed
in this material are those of the author(s) and do not necessarily
reflect the views of the National Science Foundation