
CMUCS03166
Computer Science Department
School of Computer Science, Carnegie Mellon University
CMUCS03166
A BézierBased Approach to Unstructured Moving Meshes
David Cardoze, Alexandre Cunha*, Gary L. Miller,
Todd Phillips**, Noel Walkington**
September 2003
CMUCS03166.ps
CMUCS03166.pdf
Keywords: Mesh generation, computational geometry,
Bézier curves, Bézier triangles, Bsplines,
finite element method, quadratic elements
We present in this report a new framework for maintaining good quality of
two dimensional triangular moving meshes. The use of curved elements is
the key idea that allows us to avoid excessive re nement and still
obtain good quality meshes consisting of a low number of well shaped
elements. We use Bsplines curves to model object boundaries and
objects are meshed with second order Bézier triangles. As the
mesh evolves according to a nonuniform flow velocity field, we keep
track of object boundaries and, if needed, carefully modify the mesh
to keep it well shaped by applying a combination of vertex insertion
and deletion, edgeflipping, and curve smoothing operations at each time
step. Our algorithms for these tasks are extensions of known algorithms
for meshes build of straightsided elements and are designed for any
fixedorder Bézier elements and Bsplines. We discuss a calculus of
geometric primitives for Bézier curves and triangles that we employ
to implement such operations. Although in this work we have concentrated
on quadratic elements, most of the operations are valid for elements of
any order and they generalize well to higher dimensions. We present
results of our scheme for a set of objects mimicking red blood cells
subject to a a priori computed flow velocity field. As a pure
geometric exploration, our method does not account for neither refinement
nor coarsening dictated by the simulation results.
21 pages
*Laboratory for Mechanics, Algorithms and Computing, Carnegie Mellon University
**Department of Mathematics, Carnegie Mellon University
