June 15, 2014
June 15, 2014
June 18, 2014
24.904.1 - 24.904.15
Microdynamics versus Macrodynamics – An Interdisciplinary Student ProjectProject based learning has proved to be an appropriate method to demonstrate the interaction ofmathematics, science and informatics in the engineering disciplines. A particularly suitable way ofdoing so turned out to be the establishment of interdisciplinary student projects within theframework of the Information Systems and Programming courses in close cooperation with theEngineering Mathematics courses. The students are offered a variety of project proposals at thebeginning of the semester and choose their projects according to their interests and skills. One ofthose projects, the development of computer programs for the simulation and visualization of two-dimensional incompressible fluid flows, will be presented in this paper.The behavior of a viscous incompressible fluid is governed by the simplified Navier-Stokes equations,a coupled system of nonlinear partial differential equations. While the numerical solution of linearpartial differential equations is part of the standard undergraduate engineering mathematicscurriculum, the nonlinearity of the problem made it necessary to offer supplementary lectures inorder to bridge the students’ knowledge gap. On the basis of this pledge of support, threesophomore student teams took up the challenge to simulate and visualize the flow of incompressiblefluids within the finite difference method.For comparison, another student team tackled the same problem with a cellular automatonapproach. The microscopic interactions in such lattice-gas cellular automata lead to the same form ofmacroscopic equations for the simulation of fluid flow. These models are different to the classicalfluid dynamics computations based on the discretization of partial differential equations. Theyconsider artificial micro-worlds of particles located on lattices with interactions that conserve massand momentum. From their microdynamical Boolean rules macrodynamical equations can beobtained, which reduce in suitable limits to the incompressible Navier-Stokes equations.For a better comparability of the results of the macrodynamical and the microdynamical approach, astandard example in fluid dynamics - the viscous flow driven by the tangential motion of the topboundary in a rectangular cavity - was to be simulated by all participating student teams.After a period of some conceptual difficulties, the cellular automaton project team was makingbetter progress than the teams who directly solved the Navier-Stokes equations, and managed tosimulate and visualize the flow of incompressible fluids through and around various two-dimensionalgeometries.At the end of the semester, each team was required to give a presentation to the other students ofthe class and the project advisors. Question and answer sessions following the presentations gavethe students the opportunity to discuss their approaches and methods in some detail.The projects, in general, and the visual perception of the flow fields derived from their self-madecomputer programs, in particular, have led to a deeper insight into fluid dynamics than solelyteacher-centered instruction could convey. In this paper the project work, the students’ learningprocess and its assessment will be discussed, and the outcome of the projects will be presented.
Bischof, G., & Casey, A., & Andreeva-Moschen, E. (2014, June), Microdynamics versus Macrodynamics – An Interdisciplinary Student Project Paper presented at 2014 ASEE Annual Conference & Exposition, Indianapolis, Indiana. 10.18260/1-2--22837
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