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Scalable, Shared and Distributed Memory Algorithms for Computational Solids, Fluids and Geometry

Ron Fedkiw, Stanford University

The design of numerical algorithms at the most basic and fundamental levels, leverages mathematics, applied mathematics, and computer science disciplines.  Real-world problems such as studying the effects of underbody blasts on motivate these methods for studying phenomena, such as solid material deformation, plasticity, and fracture, as well as interactions with fluids like air and water.  These algorithms are as applicable to underbody blasts as they are to the design and analysis of ship wakes or to ordnance storage and detonation, whether conventional or as used for triggers in nuclear weapons. Army researchers are the endusers of such algorithms, and so it is of utmost importance that their problems of interest are our ultimate focus when designing these algorithms.  

Figure 1:  Efficient methods for denting and bending rigid bodies, in the case where a multitude of moving and falling objects collide with each other.

Motivated by the Army’s interest in underbody blasts, design goals include numerical algorithms to address physically related problems with an aim towards not only accuracy and high fidelity, but also scalability.  Many numerical algorithms that are designed for now-defunct single-core, serial computers use a myriad of ad-hoc approaches to address the largest scale supercomputers mostly for DoE-oriented applications.  These ad-hoc approaches to scalability do in fact help, but it takes a vast number of extra cores to solve moderate-sized problems.  In reality, we would like to solve complex problems on a moderately-sized computer.  This requires readdressing the numerical approach at the most basic level.  Some of the findings are rather obvious in hindsight, such as the fact that the standard AMR approach, which is used to retain structure, typically ends up being completely unstructured on real-world problems, diminishing any gains over fully unstructured approaches.  Thus, we have gone back to chimera grids, which formerly lacked mathematical sophistication.  The research has worked to overcome these issues, especially for two-way monolithic solid-fluid coupling problems and has been published in a number of top journals.  Currently, very small shrapnel and spall (from spallation) and their effects on blast and fracture problems are being simulated without the need for many tiny grid cells to resolve them.  There is very interesting experimental data of importance to the Army for these sorts of problems.

Figure 3: A high-fidelity simulation of bubble generation and dynamics for an underwater submersible fin, using a hybrid Lagrangian-Eulerian numerical method.

Figure 4:  An example of outreach work, where students modeled and simulated a multi-body vehicle (here, a Jeep flying an Army flag) and integrated it into a real-time, interactive physical simulation that could be run on mobile devices.