Supercomputing Institute Research Bulletin Summer 1997

Mesoscale Fluid Dynamics Modeled on the T3E

There are many ways of simulating fluid dynamical phenomena that occur in nature-for example, by the finite-difference, finite-elements and spectral methods, which all approach fluid dynamics from a continuum point of view. However, there are other ways of looking at fluid motions at intermediate or mesoscales ranging from hundreds of angstroms to hundreds of microns, One method, called molecular dynamics, employs particles which are subject to a give two-body potential. As applied to mesoscale fluid dynamics, this method is rather young and is useful in treating phenomenon taking place in interfaces and cracks, or problems with large contrasts in physical priorities. For example, the molecular dynamics method has been used by scientists in Los Alamos to study problems in fracture mechanics that cannot be solved by conventional continuum methods. Dr. David A. Yuen, a Supercomputing Institute Fell, has been working with computational scientists Drs. Witek Alda, Jacek Kitowski, Witold Dzwinel, Marek Pogoda, and Jacek Moscinski at the Institute of Computer Science at the University of Mining and Metallurgy in Krakow, Poland to model mesoscale fluid dynamics using the molecular dynamics method. Their study focuses on a phenomenon known as the Rayleigh-Taylor instability problem, which involves the development of instabilities when heterogeneous fluids with vastly different physical properties are superimposed on one another, such as honey over milk. Rayleigh-Taylor instabilities appear in many diverse fields, ranging from magma chambers to the interiors of stars. To model two heterogeneous fluids, the researchers have used well over one million computer-modeled particles, which are divided into two "tribes." Each "tribe" has its own set of two-body potentials. which also includes an interaction potential between the two sets of particles. The trajectories of the particles are then integrated in time according to Newton's second law, which govern the future position of each atom according to the potential it presently encounters. The particle nature of the molecular dynamics method allows computer code to be parallelized readily on the Cray T3E, using the parallel-virtual machine (PVM) technique. This code scales well and, on 16 processors of the Cray T3E, it already runs faster than on the four processors of the Cray C90. But as fast as these massive parallel computers are, they also create a problem-how do researchers understand the massive amount of data they generate? to solve this dilemma, Yuen and his colleagues use a visualization display divice called the "Power Wall," which can handle well over seven million pixels at fast speeds. At this resolution, researchers can easily examine the fine-scale phenomena displayed on the power wall. Located at the University's Laboratory for Computational Science and Engineering, the Power Wall is a 6.5 by 8 foot display. Drs. Alda and Dzwinel traveled to the United States in April to work at the University of Minnesota. During their visit, they produced some very interesting images showing the development of secondary instabilities within the Rayleigh-Taylor primary instabilities. In their molecular dynamics simulations, the researchers employed two sets of atoms that together numbered three million. These simulations, which have been integrated for one million timesteps, are shown in figures 1 and 2. Figure 1 shows a global view of the kinetic energy distribution of this large ensemble of two-fluid flow. The most energetic portion (red color) is observed to develop near the bottom. Figure 2 shows a zoomed-in view with the development of this small-scale instabilities (red color). For mpeg movies and additional displays, consult http://banzai.msi.umn.edu:80/projects.html. With the recent increase of the T3E processors to 256, these researchers can reasonably expect to conduct molecular dynamics simulations with more than ten million particles. A greater number of processors will also allow researchers to include more physics and chemistry in the study of heterogeneous multiphase fluids in the mesoscale range. Figure 1 A global view of the simulation of 3 million particles on the Power Wall. The kinetic energy distribution in 2-D is shown here, with red being the most energetic and blue being the least energetic. Figure 2 Zoomed-in view of the development of hydrodynamic instabilities (red color)

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