alexandre cunha :: moving mesh

A Bézier-Based Approach to Unstructured Moving Meshes

David Cardoze, Alexandre Cunha, Gary Miller, Todd Phillips, Noel Walkington. In Proceedings of the 20th Symposium on Computational Geometry. June 2004, New York.

Abstract. We present a new framework for maintaining the quality of two dimensional triangular moving meshes. The use of curved elements is the key idea that allows us to avoid excessive refinement and still obtain good quality meshes consisting of a low number of well shaped elements. We use B-splines curves to model object boundaries, and objects are meshed with second order Bézier triangles. As the mesh evolves according to a non-uniform 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, edge flipping, and edge smoothing operations at each time step. Our algorithms for these tasks are extensions of known algorithms for meshes built of straight--sided elements and are designed for any fixed-order Bézier elements and B-splines. 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 precomputed flow velocity field. PDF

Animations

Meshing, fluid flow simulation, and animation codes created by Todd Phillips and David Cardoze.

Click on an image below to play the animation. NOTE: these are big size, 1024 x 768, animations so one can easily track the changes in the mesh as the simulation progresses.

Three red blood cells immersed on a parabolic flow field interacting with a static obstacle. Only flipping is used to maintain the Delaunay property on the mesh. (mpeg 8.8M)

The same example above but with edge smoothing included in the remeshing. (mpeg 7.0M)

The red blow cells above now with the full implementation: edge flipping, smoothing, refinement, and coarsening. (mpeg 8.9M)