High-fidelity, dynamic CAD model for propagating surfaces and moving meshes

We present a set of methods designed for tracking with high-order accuracy the propagation of surfaces in three dimensions with arbitrary geometric and topological complexity. Targeted applications are engineering and scientific problems for which a CAD (computer-aided design) model of the geometry is available, i.e. surface patches with high-order parameterizations as well as topological connectivity. Our method uses and maintains such a representation throughout the propagation. Validity of the dynamic boundary-representation model is ensured by handling geometric singularities. Examples are presented to demonstrate the accuracy of the pseudo-spectral method used for tracking each surface patch. A strategy for deriving a dynamic surface mesh is finally proposed for applications such as Finite Element/Volume computations with body-fitted volume grids in domains with deforming boundaries.