interactive computational sciences laboratory clarence o. e. burg assistant professor of mathematics...

Interactive Computational Sciences Laboratory

Clarence O. E. BurgAssistant Professor of MathematicsUniversity of Central Arkansas

Science Museum of MinnesotaSeptember 11, 2008

Science Museum of DiscoverySeptember 11, 2008

Clarence O. E. BurgUniversity of Central Arkansas

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Motivation for Project

Interactive investigations are superior to static presentations

Personal experience while in graduate school

PhD Advisor’s work on Smithsonian exhibit titled “How Wings Work”



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Overview of Presentation

The computational sciences process The scope of the computational

sciences Current implementation Future computational platform Current needs/plans



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The computational sciences process

The scope of the computational sciences

Current implementation Future computational platform Current needs/plans



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Overview of Computational Sciences

Develop mathematical model of physical phenomena

Represent physical domain using discrete points, called a grid or mesh

Approximately solve mathematical equations on these discrete points

Visualize, analyze and interpret the results



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Example – Water Flow in 2D

One possible system of equations

This system is well understood and the algorithms for solving it are mature

02

02

0

22

22

y

ghhv

x

huv

t

h

y

huv

x

ghhu

t

h

y

hv

x

hu

t

h



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Computational Mesh or Grid

Grid 1 (641 elements)

Grid 2 - Coarse (2564 elements)

Grid 3 - Refined (10256 elements)



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Computational Solution



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Summary of Computational Sciences

Mesh or grid generation is similar for each discipline

Visualization is similar for each discipline

Numerical schemes are well understood

Unified framework for simulating a wide variety of computational science phenomena has been developed



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The computational sciences process The scope of the

computational sciences Current implementation Future computational platform Current needs/plans



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Scope of the Computational Sciences

Almost any physical process can be modeled in 2D or 3D (except at the molecular level).

Models are based on conservation laws, so any physical process that obeys conservation laws can be modeled and simulated.

In 2D, most of these phenomena have been studied extensively via computational tools, so the algorithms are well understood and the typical interesting phenomena are well documented.



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Water Waves



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Aerospace Engineering



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Hydraulic Engineering



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Meteorology



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Electro-Magnetics



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Structural Dynamics and Mechanics



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Underground Phenomena



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Current Status Interface for selection

Cases Solver options Physical parameters

Computational Solver Air flow equations Water flow equations (as seen from

above) Visualizer



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Shallow Water Interface



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Images from simulation of channel contraction (flow from left to right)

Early in simulation Waves form within contraction

Waves begin to stabilize Final solution

Water depth is shown, red and white are high levels of water, while blue and black are low levels



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In-flow speed increased by approximately 20%

Solution from previous simulation

Increased flow rate forcing out slower and deeper water

Final Solution



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Compressible (Air) Interface



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Supersonic regimes for transonic flows



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Transonic NACA 00124 deg, Ma = 0.75

Density Mach Number



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Transonic NACA00120 deg, Ma=0.75

Density Mach Number



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Shock waves from supersonic wing



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Supersonic NACA 00124 degrees, Ma = 1.50

Density Mach Number



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Field Test Summer 2008, Math department held a

weekly math camp for high school students These two computational packages were

used Lessons learned

The three codes need to be integrated within one package

Students quickly figured out how to use interface More guidance is needed to make these tools

effective educationally.



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sciences Current implementation Future computational

platform Current needs/plans



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Computational Platform Sony Playstation 3

Uses Cell Broadband Engine processor Performs math computations at

roughly 15-20 times faster than a single processor PC

Used in Dept of Energy’s Roadrunner supercomputer, the world’s fastest

Software must be completely redesigned and rewritten

Limited memory

Due to speed and limited memory, this machine is perfect for 2D interactive computational simulations



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Current Needs/Plans Merge the three programs into one

program Internet based Sony PS3 based

Discipline specific expertise Expertise in designing and developing

effective museum exhibits Increase scope and depth for

computational sciences platform



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Thanks!

interactive computational sciences laboratory clarence o. e. burg assistant professor of mathematics...

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