Fluid Dynamics Simulation Using Cellular Automata

Gunter Bischof; Christian Steinmann

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Conference: 2012 ASEE Annual Conference & Exposition
Location: San Antonio, Texas
Publication Date: June 10, 2012
Start Date: June 10, 2012
End Date: June 13, 2012
ISSN: 2153-5965
Conference Session: Using Applications and Projects in Teaching Mathematics
Tagged Division: Mathematics
Page Count: 14
Page Numbers: 25.642.1 - 25.642.14
DOI: 10.18260/1-2--21399
Permanent URL: https://peer.asee.org/21399
Download Count: 4169

Paper Authors

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Gunter Bischof Joanneum University of Applied Sciences, Graz, Austria

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Throughout his career, Günter Bischof has combined his interest in science, engineering and education. He studied physics at the University of Vienna, Austria, and acquired industry experience as development engineer at Siemens Corporation. Currently, he teaches Engineering Mathematics and Fluid Mechanics at Joanneum University of Applied Sciences. His research interests focus on vehicle aerodynamics, materials physics, and engineering education.

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Christian Steinmann Joanneum University of Applied Sciences, Graz, Austria

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Christian Steinmann has an engineer degree in mathematics from the Technical University Graz, where he focused on software quality and software development process assessment and improvement. He is Manager of HM&S IT-Consulting in Graz and provides services for SPiCE/ISO 15504 and CMMI for development as a SEI-certified instructor. He performed more than 100 process assessments in software development departments for different companies in the finance, insurance, research, automotive, and automation sector. Currently, his main occupation is a consulting project for process improvement at the Electrics/Electronics Development Department at Volkswagen in Wolfsburg, Germany. On Fridays, he is teaching computer science introductory and programming courses at Joanneum University of Applied Sciences in Graz, Austria and has for 14 years.

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Abstract

Fluid Dynamics Simulation using Cellular AutomataThe idea to apply project-based learning as a didactical method in the freshman year wasprimarily driven by the need to motivate the students to apply theoretical knowledge inpractice as early as possible. Faculty teaching in the areas of mathematics, science andinformation technology noted that students were not always enthusiastic in approaching thetheoretical concepts involved in these disciplines, and that they frequently failed to recognizethe interrelatedness of what they were studying as well as its applicability to their futureprofessions. Therefore, these members of faculty get together and define every year a series ofprojects which incorporate elements of their respective syllabi. The students are confronted,complementary to their regular courses, with problems that are of a multidisciplinary natureand demand a certain degree of technical proficiency.In the last academic year a particularly challenging problem was posed on those first-yearstudents, who have, according to their interests, chosen the Lattice-Gas Cellular Automatonproject. Their task was the implementation of the lattice-gas model of Frisch, Hasslacher, andPomeau (the FHP model) in a computer program for the visualisation of two-dimensionalfluid density and velocity distributions. In this model, particles can move with the samevelocity at each site of the residing triangular lattice in any of six possible directions. Anexclusion principle, which states that at any given site no two particles can have the samevelocity, puts a stringent constraint on these velocities. Therefore, a site may be empty oroccupied by up to six particles. Each time step consists of a collision and a streaming phase.Collision occurs synchronously at the lattice nodes, while the streaming takes place on theconnection between each two nodes. The collision rules are chosen in such a way that massand momentum are conserved. By multi-scale analysis it can be shown that the FHP modelasymptotically goes over to the incompressible Navier-Stokes equation.The students worked in teams of three, and three groups were assigned the same task in orderto introduce a competitive aspect, which increased the students’ motivation. The members offaculty who have proposed the project supervised and supported the students. The progress ofthe work was continuously evaluated in order to ensure an appropriate time management. Theoutcomes of the projects were deemed successful, although only one group exhaustivelyaccomplished the task.In this paper the project work, the students’ learning process and its assessment will bedescribed, the outcome of the project will be presented and the effect on the students’ furthereducation will be discussed.

Citation
Format

Bischof, G., & Steinmann, C. (2012, June), Fluid Dynamics Simulation Using Cellular Automata Paper presented at 2012 ASEE Annual Conference & Exposition, San Antonio, Texas. 10.18260/1-2--21399

TY  - CPAPER
AB  - Fluid Dynamics Simulation using Cellular AutomataThe idea to apply project-based learning as a didactical method in the freshman year wasprimarily driven by the need to motivate the students to apply theoretical knowledge inpractice as early as possible. Faculty teaching in the areas of mathematics, science andinformation technology noted that students were not always enthusiastic in approaching thetheoretical concepts involved in these disciplines, and that they frequently failed to recognizethe interrelatedness of what they were studying as well as its applicability to their futureprofessions. Therefore, these members of faculty get together and define every year a series ofprojects which incorporate elements of their respective syllabi. The students are confronted,complementary to their regular courses, with problems that are of a multidisciplinary natureand demand a certain degree of technical proficiency.In the last academic year a particularly challenging problem was posed on those first-yearstudents, who have, according to their interests, chosen the Lattice-Gas Cellular Automatonproject. Their task was the implementation of the lattice-gas model of Frisch, Hasslacher, andPomeau (the FHP model) in a computer program for the visualisation of two-dimensionalfluid density and velocity distributions. In this model, particles can move with the samevelocity at each site of the residing triangular lattice in any of six possible directions. Anexclusion principle, which states that at any given site no two particles can have the samevelocity, puts a stringent constraint on these velocities. Therefore, a site may be empty oroccupied by up to six particles. Each time step consists of a collision and a streaming phase.Collision occurs synchronously at the lattice nodes, while the streaming takes place on theconnection between each two nodes. The collision rules are chosen in such a way that massand momentum are conserved. By multi-scale analysis it can be shown that the FHP modelasymptotically goes over to the incompressible Navier-Stokes equation.The students worked in teams of three, and three groups were assigned the same task in orderto introduce a competitive aspect, which increased the students’ motivation. The members offaculty who have proposed the project supervised and supported the students. The progress ofthe work was continuously evaluated in order to ensure an appropriate time management. Theoutcomes of the projects were deemed successful, although only one group exhaustivelyaccomplished the task.In this paper the project work, the students’ learning process and its assessment will bedescribed, the outcome of the project will be presented and the effect on the students’ furthereducation will be discussed.
AU  - Gunter Bischof
AU  - Christian Steinmann
CY  - San Antonio, Texas
DA  - 2012/06/10
PB  - ASEE Conferences
TI  - Fluid Dynamics Simulation Using Cellular Automata
UR  - https://peer.asee.org/21399
DO  - 10.18260/1-2--21399
ER  -