David A. Yuen, Fellow

Numerical Simulations of Geophysical Phenomena

High Rayleigh number three-dimensional convection for the Earth’s mantle from Rayleigh number 106 through 1010 with the highest resolution of 601x601x601 grid points.

These researchers worked on several large-scale computational problems that required both the speed and memory resources of vector and massively parallel computers. Some of the most significant problems addressed by this group were the following:

• Three-dimensional mantle convection with variable thermal conductivity and viscosity
• Mixing dynamics in convection
• Molecular dynamics and dissipative particle dynamics as applied to multiphase flow with 107 particles
• Visualization of large data sets
• Numerical modeling of the Earth’s lithosphere- mantle system with complicated physics and rheology
• Three-dimensional convection in a spherical shell

The following provides an overview of some of the work performed by this group

One area of interest for this group is secondary upwelling instabilities developed in high Rayleigh number convection. In this area, possible applications to hot spots were observed through conducted numerical experiments for mantle convection in an axisymmetrical spherical- shell geometry from Rayleigh numbers ranging from three million to ten billion for a purely basal heating configuration. For Rayleigh numbers between around 30 million and one billion, a string of these secondary instabilities can develop from a single plume. Analysis of the spectrum of wavelength associated with the fold instabilities showed that there is a window in the Rayleigh number between around ten million and one billion where these secondary folding instabilities would develop. These results, when applied to the upper mantle, may explain the formation of hotspots in a turbulently convecting uppermantle with a Rayleigh number greater than ten million.

Blood cells clotting in bifurcating capillary vessel simulated by using discrete particles. The blood cells are modeled by particles on strings. The plasma fluid is represented by a fluid particle model. Plasma velocity is the lowest at the choking point. The vessel diameter is 15–20 micrometers and the hematocrit is 10%. The Reynolds number, Re, is approximately 0.01. This simulation used two million particles, and was created using the AMIRA package.

This group also studied dissipative particle dynamics (DPD). DPD and its generalization —fluid particle model (FPM)—represent the “fluid particle” approach for simulating fluid-like behavior in the mesoscale. Unlike particles in the molecular dynamics method, the fluid particle can be viewed as a “droplet” consisting of liquid molecules. In FPM, fluid particles interact by both central and non-central, short-range forces with conservative, dissipative, and Brownian character. This group discovered that the efficiency of the FPM code depends strongly on the number of particles simulated, geometry of the box, and the computer architecture. This FPM code can be applied for simulating mesoscopic flow dynamics in capillary pipes or critical flow phenomena in narrow blood vessels.

Another project for this group involved developing a method for data mining. Current advances in computer hardware, information technology, and data collection techniques have produced very large data sets in a wide variety of scientific and engineering disciplines. The group implemented a map-like approach to retrieve useful information from geophysical and geological data: spatial data is mapped onto a two-dimensional grid from which the user can quiz the data with the map interface as a user extension. The data is stored on the server, while the computational gateway separating the user and the server can be the front end of an electronic publication, an electronic classroom, a survey, or an e-business. The group used a combination of java, java3d, and perl for processing the data and communicating between the user and server. The user can interrogate the geospatial data over any particular region with arbitrary dimensions and then receive back relevant statistical analysis, such as histogram plots and local statistics. The group has used this method for distribution of prime numbers, two-dimensional mantle convection, three-dimensional mantle convection, high-resolution satellite reflectance data over multiple wavelengths, and molecular dynamics describing the flow of blood in narrow vessels.

Other topics of study for this period included: the problem of viscoelastic relaxation of the earth solved by a matrix eigenvalue approach based on discretization in grid space; rheological structure and deformation of subducted slabs in the mantle transition zone with implications for mantle circulation and deep earthquakes; and modeling of viscoelastic plumelithosphere interaction using adaptive multilevel wavelet collocation method.

Research Group

Stephen Y. Bergeron, St. Albert, Quebec, Canada
John Boggs, Staff
Kris (Christopher) Boryczko, Computer Science Department, Mining and Computer Institute, Krakow, Poland
Laszlo Cserepes, Geophysics Department, Eotvos University, Budapest, Hungary
Fabien Dubuffet, Supercomputing Institute Research Scholar
Witold Dzwinel, Research Associate
Gordon Erlebacher, School of Computational Sciences and Information Technology, Department of Mathematics,
Florida State University, Tallahassee, Florida
Hiromi Fujimoto, Research Center for Prediction of Earthquakes, Graduate School of Science, Tohoku University, Aoba-ku Sendai, Japan
Zachary A. Garbow, Supercomputing Institute Undergraduate Intern
Dan Goldstein, Department of Aerospace and Mechanical Engineering, University of Missouri, Columbia, Missouri
Ulli Hansen, Institut für Geophysik, Universität Münster, Münster, Germany
Ladislav Hanyk, Department of Geophysics, Karlova University, Troja, Prague, Czech Republic
Cathy Hier-Majumder, Research Associate
Motoyuki Kido, Ocean Research Institute, University of Tokyo, Tokyo, Japan
Alexander Kritski, Centre for Marine Science and Technology, Curtin University, Perth, Western Australia
Marc Monnereau, CNE/CNRS, Toulouse, France
Yuri A. K. Podladchikov, Geologisches Institute, ETH-Zürich, Zürich, Switzerland
Emma Rainey, Undergraduate Student Researcher
Klaus Regenauer-Lieb, Hohentengen, Germany
Billy Richard, Centre National d’Etudes Spatiales, Paris, France
James R. Rustad, MSIN K8-96, Pacific Northwest National Lab, Richmond, Washington
Bertram Schott, Department of Earth Sciences, Uppsala University, Uppsala, Sweden
Erik Sevre, Research Associate
Arkady Ten, Visiting Researcher
Arie P. van den Berg, Theoretical Geophysical Department, University of Utrecht, Utrecht, Netherlands
Oleg Vasilyev, Department of Mechanical & Aerospace Engineering, University of Missouri-Columbia, Columbia, Missouri
Ludek Vecsey, Graduate Student Researcher
Alain P. Vincent, CERCA, Montreal, Quebec, Canada
Tomoyuki Yamamoto, Institute of Physics and Chemistry, Tokyo, Japan
Tomo Yanagawa, Department of Earth and Planet Sciences, Kyushu University, Fukuoka, Japan
Lilli Yang, Undergraduate Student Researcher
Dapeng Zhao, Institute of Geodynamic Research, Ehime University, Matsuyama, Japan