Geophysical mass flows—debris flows, volcanic avalanches, landslides—are often initiated by volcanic activity. These flows can contain ${\text{O(10}}^6{\text{–10}}^7\mathrm{)\hspace{0.17em}}{\mathrm{m}}^3$ or more of material, typically soil and rock fragments that might range from centimeters to meters in size, are typically $\text{O(10\hspace{0.17em}}\mathrm{m})$ deep, and can run out over distances of tens of kilometers. This vast range of scales, the rheology of the geological material under consideration, and the presence of interstitial fluid in the moving mass, all make for a complicated modeling and computing problem. Although we lack a full understanding of how mass flows are initiated, there is a growing body of computational and modeling research whose goal is to understand the flow processes, once the motion of a geologic mass of material is initiated. This paper describes one effort to develop a tool set for simulations of geophysical mass flows. We present a computing environment that incorporates topographical data in order to generate a numerical grid on which a parallel, adaptive mesh Godunov solver can simulate model systems of equations that contain no interstitial fluid. The computational solver is flexible, and can be changed to allow for more complex material models, as warranted.

Computer-aided design and finite element methods (FEM) have interested dental researchers because of its use in the computer simulation and design of dental implants, a process greatly facilitated by the development of new computer technology and more accurate modeling technologies. FEM allows for a better understanding of stresses along the surfaces of an implant and in surrounding bone. This will aid in the optimization of implant design and placement of the implant into the bone; it will also help when designing the final prostheses to minimize stresses. The purpose of this review is to elucidate the role of FEM and the impact of this technology in clinical dentistry in the new millennium.

We present a framework for modeling a dry geophysical mass of granular material -- a debris or volcanic avalanche or landslide -- flowing over an erodible surface. We also describe a computing environment that incorporates topographical data into a parallel, adaptive mesh computational algorithm that solves the model equations.