CFD Collaboratory   

Introduction: Through the CFD Laboratory, the UT College of Engineering offers an internationally recognized computational engineering sciences  (CES) graduate curriculum leading to MSc and PhD Engineering Science degrees. The fully enabled Internet website fully enables outreach to the professional community in an absolutely time- and distance-insensitive mode for professional study.  Upon acceptance to the UT Graduate School, the formal option leads to the Graduate CFD Certificate following completion of 12 graduate credit hours in the CES curriculum. The second option, conducted directly through the CFD Laboratory, enables full professional participation in these courses, without Graduate School association leading to a CFD Laboratory Certificate of Course Completion. Finally, the third option enables professional self-study independent of a CFD Laboratory association.

Professional Study:

Courses: Archived courses available for professional study are open for topical review at the Internet website (http://cfdlab.utk.edu/Internet). All courses are completely self-contained with video-streamed lectures, supporting courseware, problem and computer exercises and their archives. Touching the appropriate hot word on this page leads to course website for content perusal.

• ME 452w: Finite Element Analysis (3): A senior level undergraduate course on FEA covering topics in heat transfer, structural mechanics, fluid mechanics, mechanical vibrations and heat/mass transport. Students are expected to have completed the first UG courses in the four lead subjects. Over a dozen computer lab experiments are envolved based on the Matlab and COMSOL problem solving environments. Its a great place to "get your arms around" FEA methodology! Read about the content.

• ES 551w: The Computational Engineering Sciences (3): A thorough first-level graduate exposure to the mathematics underlying weak form constructions of approximate solutions to elliptic boundary value problems permeating engineering mechanics. All theorization is thus completed in the continuum, after which only! is a spatially discrete implementation developed. The focus is on validation of the available theoretical error estimates, in both space and time, and direct comparison of finite difference, finite volume and finite element implementations. A dozen Matlab-based computer lab experiences complement the course thorough content in the computational engineering sciences.

• ES 552w: Computational Fluid/Thermal Sciences (3): The succeeding second level (ES551 is the prerequisite) graduate development of the mathematics underlying weak form construction of approximate solutions to the thermal-fluid problem statements permeating mechanical, civil and aerospace engineering. Again all theorization is completed in the continuum, followed by spatially discrete implementations via finite element/difference/volume methods. Integrated computer labs focus on validation of the theoretical assertion that the finite element discrete implementation leads to the optimal solution!  Formal stability analyses lead to modified Galerkin formulations, again theorized in the continuum, leading to optimal methodology for non-linear fluid-thermal Navier-Stokes systems including turbulence closure, conjugate heat transfer, artificial diffusion and solution-adaptive mesh optimal constructions.

• ES 645w: Advanced Topics in Turbulence (3): A rigorous and thorough exposure to the fundamentals of turbulence theory underlying the wide range of closure systems embedded in commercial, national and proprietary CFD codes. For the time-averaged (RANS) Navier-Stokes manipulation, coverage includes a thorough exposure to boundary layer similarity theory leading to algebraic, two-equation, and Reynolds stress transport systems . For the spatially filtered (LES) Navier-Stokes manipulation, coverage includes the classic subgrid-scale (SGS) tensor model formulations transitioning to the wavenumber asymptotics theory which leads to analytical closure for the four identified Reynolds stress tensors. The course is complemented with focused computer lab experiences.

Options:: In addition to the UT Graduate CFD Certificate, detailed next, two options exist for professional study as follows.

1. Strictly self-study: DVD sets of the archived course lectures along with the lecture courseware file are available for all four Internet enabled courses. Any of these may be purchased directly from the publisher, contact www.jcomputek.com

2. Participatory study: The requested course is made available for three months from a start date, and the participant may elect this period to coincide with the scheduled UT academic semester course, which enables collegial interaction with the “live” class. A CFD Laboratory Certificate of Completion is issued upon successful performance. For students registered at a university awarding academic credit for this option, CFD Lab will submit requested certification of successful completion of the course. Independent of timing, the course charge is US $995 payable directly via check to “CFD Laboratory” and mailed to UT CFD Laboratory, 316A Perkins Hall, Knoxville TN 37996-2030. Include an email contact with the submission along with selection of the desired course and start date.

3. Collegial interaction: For academics holding a university faculty appointment, the charge for option 2 is halved and full collegial interaction with the CFD Lab academic staff is available.

Support Materials: The text supporting ME 452 and ES 551 is available from the UT Bookstore or directly from the publisher, www.jcomputek.com The original text for ES 552, published in 1983, is out of print with the replacement edition now in draft. A CD containing the first six chapters of this manuscript is available at no charge with course application. The three texts for ES 645 are available from their respective publishers. All academic materials at the website are the intellectual property of the UT CFD Laboratory and enjoy full copyright protection.

CFD Certificate:

Graduate Certificate in CFD:
The UT Graduate School, through the College of Engineering, offers a formal graduate certificate in computational fluid dynamics (CFD).  This academic program is designed for the practicing engineering professional with the desire to develop dexterity in CFD with formal recognition. All required academic material is archived at the UT CFD Laboratory website, hence available on demand on a totally flexible schedule.

The Graduate Certificate in CFD requires accumulation of 12 graduate credit hours. The base requirement is completion of the three course sequence ES 551, ES 552 and ES 645, which are extensively cross-listed among departments in the College of Engineering. The fourth course is optional, to be approved by CFD Laboratory. It is suggested to be the first level academic graduate course in Fluid Dynamics which may be transferred to UT for credit from a local university.   The following Powerpoint file summarizes the scope and content of the three ES course sequence.

The sole academic prerequisite for entering the graduate certificate program is a bachelors degree in engineering or the applied sciences.  Applicants must seek admission to the UT Graduate School and become admitted thereto.

Pedagogical Outreach:

The recently published text The Computational Engineering Sciences  (ISBN 0-9790459-0-8) is the third authored by Prof. Baker on this subject. It presents and summarizes in concise engineering terminology the current state of theory and computer practice of discrete implementations of weak form constructions in the computational engineering sciences. The text frontispiece material is viewable here .

Unique for a text on this subject, The Computational Engineering Sciences develops an object-oriented template syntax which organizes all aspects of FE-implemented weak forms into a computer-compatible instruction set. The text fully integrated hands-on computer experiments are totally Matlab® enabled via the text included FEmPSE "toolbox." This basic syntactical organization of the 6 data types intrinisc to FE implementations is certainly extensible to a problem statement of your specific interest. The included DVD contains the full compliment of computer lab execution .m files.

Professor Baker’s follow-on authorship activity is replacement of the pioneering 1983 textbook Finite Element Computational Fluid Mechanics. In support of the ES 552 course, the draft is now complete through 6 chapters and will appear under the title Optimal Modified Galerkin Weak Form CFD. The frontispiece draft for the text will appear here in the near term..

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