ITR/ACS: Simulation of Flows with Dynamic Interfaces on
Multi-Teraflop Computers
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Guy E. Blelloch, Omar Ghattas, Gary L. Miller,
Noel J. Walkington, James F. Antaki,
Bartley P. Griffith, Marina V. Kameneva Robert L. Kormos,
William R. Wagner, ZhongJun Wu, George M. Turkiyyah.
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Overview :
We propose to develop advanced parallel geometric and numerical algorithms and software for simulating complex flows with dynamic interfaces. The development of scalable, parallel high-accuracy algorithms for simulating such flows poses enormous challenges, particularly on systems with thousands of processors. We will use the resulting tools to simulate blood flowin artificial heart devices. This application provides an excellent testbed for the methods we develop: simulation-based artificial organ design is extremely computationally challenging and of critical societal importance.
Flows with dynamic interfaces arise in many fluid-solid and fluid-fluid interaction problems, and are among the most difficult computational problems in continuum mechanics. Examples abound in the aerospace, automotive, biomedical, chemical, marine, materials, and wind engineering sciences. These include large-amplitude vibrations of such flexible aerodynamic components as high aspect ratio wings and blades; flows of mixtures and slurries; wind-induced deformation of towers, antennas, and lightweight bridges; hydrodynamic flows around offshore structures; interaction of biofluids with elastic vessels; and materials phase transition problems. We are particularly interested in modeling the flow of blood, which is a mixture of interacting solid cells and fluid plasma. Current blood flow models are macroscopic, treating the mixture as a homogeneous continuum. Microstructural models resolve individual cell deformations and interactions with the surrounding fluid plasma. Because of the computational difficulties of resolving tens of thousands of deforming cellular interfaces, no one to date has simulated realistic blood flows at the microstructural level. Yet such simulations are necessary in order to gain a better understanding of blood damage which is central to improved artificial organ design and for the development of more rational macroscopic blood models.
Parallel flow solvers on fixed domains are reasonably well understood. In contrast, simulating flows with dynamic interfaces is much more difficult. The central challenges are to develop numerical algorithms that stably and accurately couple the moving fluid and solid domains and resolve the deforming interfaces, and geometric algorithms for evolving and managing the resulting dynamic particle/mesh systems. The associated dynamic data structures are particularly troublesome on highly parallel computers, which are made necessary by the complexity of many applications. Most current methods approach the difficulties of dynamic interfaces by computing the flow on a fixed, regular grid. The effect of the dynamic interfaces is then incorporated either through some type of constraint or force representing the interface, or through an auxiliary field variable that signifies the presence of fluid or solid material at a spatial point. Parallelizing these methods is relatively straightforward, since the flow is computed on a fixed grid. However, the resulting fixed resolution is a serious disadvantage if one wants to vary resolution sharply within the grid. This is the case for example when local interfacial dynamics are critical, as in blood flow or phase change problems.
Our approach is radically different. We will treat the fluid and solid domains as collections of particles, with associated meshes, that evolve over time, and devise numerical algorithms that couple the fluid and solid together seamlessly. We will attack the difficulty of generating and managing a constantly evolving mesh/particle system by creating fundamentally new highly parallel and scalable algorithms for the convex hull, Delaunay triangulation, meshing, partitioning, and N-body components. Our preliminary 2D work demonstrates that the resulting geometric computations can be made very cheap compared to numerical computations. Despite the conventional wisdom on parallel dynamic mesh methods, we believe that with careful attention to fundamental algorithmic issues flow simulations on constantly evolving domains can be made to scale to the thousands of processors that characterize multi-teraflop systems.
While microstructural blood flow modeling will serve as our first application, the computational algorithms and software we create will be more widely applicable to a variety of fluid solid inter-action problems. More generally, the core parallel computational geometry kernels convex hull, Delaunay triangulation, coarsening/refinement, partitioning, N-body provide generic support for the geometric computations underlying many dynamic irregular problems. We will create and publically distribute a portable library of efficient implementations of these algorithms. Much as the PETSc library has greatly simplified the task of programming parallel PDE solvers by providing many of the necessary numerical kernels, we envision a library of parallel geometric kernels being of great benefit across a wide range of scientific computing problems that involve dynamic meshes.
We have assembled a multidisciplinary team that combines Carnegie Mellon s leadership in computer and computational science with the University of Pittsburgh Medical Center s world-class program in artificial organs. This project will support 11 graduate students and a group of un-dergraduates. These students will be part of a new program at CMU in Computational Science and Engineering that we are in the process of establishing. The proposed project will also be part of that program, and we believe will serve as an archetype of how applications, computational, computer, and mathematical scientists can work together to tackle societal problems that cannot be addressed solely from the vantage of any one discipline. Moreover, we intend to communicate our work to the broader public (as we have done in the past), in the process demonstrating how high end computing can contribute to improving the health of our society.
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