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Fluid Dynamics Simulation Using Cellular Automata

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2012 ASEE Annual Conference & Exposition


San Antonio, Texas

Publication Date

June 10, 2012

Start Date

June 10, 2012

End Date

June 13, 2012



Conference Session

Using Applications and Projects in Teaching Mathematics

Tagged Division


Page Count


Page Numbers

25.642.1 - 25.642.14



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Paper Authors


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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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.

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

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