Animated Viscoplastic Materials with Dynamically Changing Meshes

We intend to develop fast, versatile, and accurate computational models for viscoplastic materials ranging from stiff, non-compliant solids to low viscosity fluids. We are designing these models for applications where visual realism, computation speed, and robustness are the predominant requirements (with numerical accuracy being subordinate). Examples of such applications include real-time interactive training simulations (e.g. surgical simulation or hazardous duty simulations) and offline generation of visualizations (e.g. cinematic effects or accident reenactment).

To achieve this goal, we must develop fast, guaranteed-quality methods for generating and incrementally updating unstructured (irregular) triangular and tetrahedral meshes. Dynamically changing meshes are a necessity to model the complete range of viscoplastic materials, especially where large deformations and mixing may occur. Thus, the actions of the numerical simulation and the remeshing algorithms must be tightly integrated, especially if we wish to minimize errors due to interpolation and reinterpolation. To ensure that our dynamic meshing algorithms and implementations are useful for other applications as well, we will develop a general methodology for communicating information between the numerical simulation and the mesh generator.

Our educational objectives complement our research objectives. The PIs will develop and teach courses on physically based modeling and mesh generation. The materials covered in these courses will be closely related to current research topics. Both graduate and undergraduate students will participate in research activities. More advanced graduate student researchers will have the opportunity, and be encouraged to mentor undergraduate and junior graduate students. The second PI is authoring a textbook on Delaunay mesh generation. The text will include the fundamentals of dynamic mesh generation that we learn during the course of the proposed research.