Introductory Fluid Mechanics (ME331/NE331)

This is a required junior level course on fluid mechanics and second in the Thermal Fluid Sciences (TFS) sequence. This course deals with fundamentals of fluid mechanics and involves theoretical analysis and conceptual understanding of fluid flow problems. Topics covered include hydrostatics and stability of floating objects, conservation laws in the integral and differential forms, flow kinematics, dimensional analysis, laminar and turbulent flow through pipes and pipe networks, drag and lift forces due to external flow over immersed objects.

Fluid mechanics involves several differential and integral equations and requires knowledge of calculus and mathematical analysis. Instructions typically involve relating the mathematical equations to fundamental concepts. Exams are designed to test conceptual understanding of the subject and typically are * not *tests of memory.

Mechanical Engineering Methods (ME373/ME373H)

This is a required junior level course on analytical and numerical methods to solve mechanical engineering problems. Topics covered include solutions to ordinary differential equations, systems of equations, Taylor series and finite differencing, Fourier analysis, and introduction to partial differential equations. Emphasis is placed on accuracy of numerical methods and use of appropriate schemes for different types of problems encountered in Mechanical Engineering. Dr. Apte was the first to propose honors section (ME373H) of this course. This proposal was approved by the Honors College (2009) and Dr. Apte will plan to offer honors section of this course in the future.

Proficiency in Matlab programming is essential. Emphasis is placed on homework and computer projects.

Numerical Methods for Engineering Analysis (ME575/NE526)

This is a required course for first year graduate students in Thermal-Fluid Sciences. The topics covered include numerical interpolation, differentiation and integration, ordinary differential equations, initial and boundary value problems, systems of equations, elliptic and parabolic partial differential equations, simple hyperbolic systems and convective-diffusive problems. Emphasis is placed analytical tools such as stability analysis and modified wavenumber analysis to understand the limitations of different numerical approaches and to facilitate appropriate choice of a numerical scheme for a particular application. Examples span different areas in mechanical systems, RLC electrical systems, heat transfer, fluid flows, chaos and dynamics, wave propagation, weather prediction, predator-prey ecosystem, quantitative finance, among others.

Familiarity with linear algebra and elementary differential equations is necessary. Students write their own computer programs, typically in Matlab; however, this course provides an excellent opportunity to learn and practice (on your own) scientific programming language such as Fortran90.

Computational Fluid Dynamics (ME667)

This is an advanced graduate level course dealing with finite volume methods for incompressible fluid flow and scalar transport problems. Emphasis is placed on the conservation properties of fluid flow equations and relevance to numerical methods, scalar transport and convective-diffusive systems, fractional step schemes, co-located and staggered grid arrangements, error quantification and stability of numerical methods. Applications include variety of fluid flow and heat transfer problems. Special topics covered also include basic introduction to variable density flows, immersed boundary method, and simulations of turbulent flows (such as direct and large-eddy simulation).

This course is intended for students from different disciplines (mechanical, civil, applied math, ocean engineering, physical oceonagraphy, atmospheric and environmental sciences etc.) interested in development and application of numerical algorithms to a variety of problems involving fluid flow and scalar transport. Emphasis is placed on physical understanding of the numerical methods. Proficiency in programming is not required; however, you are required to write your own computer programs.

Turbulence Modeling (ME5xx)

This is a new course that will be offered every other year starting Spring 2009 (taught as ME569, title change pending). This course provides an overview of turbulence modeling techniques for the prediction of turbulent flows. Emphasis is placed on turbulence simulation techniques such as direct numerical simulation (DNS), large-eddy simulation (LES), and Reynolds-averaged Navier Stokes (RANS) models. It also contains a review on turbulece, conservation equations for turbulent flows, Reynolds and Favre averaging and the closure problem, turbulence energy and Reynolds stress equations.

This is **not **a programming intensive course. Students will gain understanding of turbulent flows through post-processing of DNS data provided during this course. An overiew of commonly used single and two-point statistics, energy spectra, and feature identification techniques will be provided

Flow Structure Identification and Scientific Visualization (ME505)

This reading and conference course co-taught by Dr. Apte, Prof. Liburdy, and Dr. Zhang brought together graduate students from thermal fluid sciences and scientific visualization resulting in cross-fertilization of several ideas on detection of swirl, vortical structures, and singularities in unsteady separated flows. Data obtained from direct numerical simulations and experimental techniques such as time-resolved PIV on flow over bluff bodies (airfoils, square cylinder, etc.) are analyzed using standard vortex identification techniques (such as Gamma function, the lambda-2 method) and also using the approaches developed in scientific visualization community (vector and tensor field topology). More details on research work done as class projects can be obtained here.

Scientific Computing and Parallel Processing (ME5??)

This is also a new course that is being developed as special topics in fluid mechanics. The purpose of this course is to introduce students to scientific computing and parallel processing techniques. This course will introduce the parallel programming paradigm: *Message Passing Interface *(MPI). Topics covered include parallel programming using MPI, domain decomposition, scalability, latency, Amdahl's law, data structures, SIMD, MIMD. This course will involve computer laboratory demonstrations and will provide hands-on experience with parallel processing and scientific computing fundamentals.

The course is intended for graduate students; however, the course material is also suitable for senior undergraduate students interested in computational methods (seniors interested in these areas are highly encouraged to take this course as a graduate elective) . This course requires basic knowledge of Fortran or C as course assignments and projects will require programming in these languages. It also provides opportunities to learn these scientific computing languages together with MPI programming.