Teaching

Topics: Characteristics of fluids, fluid statics, elementary fluid mechanics – the Bernoulli equation, fluid kinematics, finite control volume analysis, differential analysis of fluid flow, dimensional analysis and similitude.

Textbook: Fundamentals of Fluid Mechanics, 8th Edition, Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein, ISBN: 978-1-119-08070-1

Topics: Aerodynamic forces and moments, aerodynamic coefficients, steady flight analysis, conservation equations of fluid flow in integral and differential forms, nondimensional numbers, dimensional similarity, Bernoulli’s equation, fundamentals of inviscid incompressible flow, vorticity and divergence, Laplace’s equation for the stream function and velocity potential, classical potential solutions, drag generation, circulation, Kutta-Joukowski theorem, incompressible flow over airfoils, Kutta condition, Kelvin’s circulation theorem, lift generation, classical thin airfoil theory, vortex panel method, incompressible flow over finite-span wings, Prandtl’s classical lifting-line theory, lifting-surface theory, vortex lattice method, high-speed aerodynamics, subsonic compressibility corrections.

Textbook: Fundamentals of Aerodynamics, 6th Edition, J. D. Anderson, McGraw-Hill Education, ISBN 1259129918

Topics: Heat equation, ODEs, PDEs, boundary and initial conditions, method of separation of variables, solving the heat equation in 1D, interpretation and applications of the heat transport equation, eigenfunctions and eigenvalues, introduction to Fourier series, expansion of a function in Fourier series (Fourier sine and cosine series), physical interpretation of Fourier series, principles of continuity and extension of a function, derivation of the wave equation in 1D and 2D, analytical solutions in 1D, higher dimensional PDEs (for plates, cylinders, and spheres), vibrations in a rectangular membrane, application of the heat equation in 2D and 3D to find the temperature of a point in a plate and a cube, application of the wave equation to solve vibration problems of rectangular plates, double Fourier series and orthogonality, vibrations of a circular membrane, Bessel functions, the Sturm-Liouville eigenvalue problem.

Textbook: Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, 5th Edition, Richard Haberman

Topics: Discretization techniques, finite differences, implicit and explicit approaches, stability conditions, governing equations of fluid mechanics, conservative and primitive forms, closure, boundary conditions, well-posedness, strong conservation form, numerical solutions of compressible and incompressible Navier-Stokes equations, finite volume methods on structured and unstructured grids, pressure correction, SIMPLE algorithm, turbulence modeling, Reynolds-averaged and filtered Navier-Stokes equations, eddy viscosity, subgrid-scale models.

Textbook: Computational Fluid Dynamics: The Basics with Applications, 1st Edition, J. D. Anderson, ISBN-13: 978-0070016859, ISBN-10: 0070016852

Topics: Potential theory, canonical viscous flows, time-dependent viscous flows, very viscous flows, boundary layer theory.

Textbooks: Elementary Fluid Dynamics, Oxford Applied Mathematics and Computing Science Series, 1st Edition, D. J. Acheson, ISBN-10: 0198596790

Topics: Vandermonde matrices, matrix-vector multiplication, orthogonal vectors and matrices, norms, singular value decomposition (SVD), projectors, QR factorization, least squares problems, conditioning and condition numbers, floating point arithmetic, numerical stability, Gaussian elimination, pivoting, Choleski factorization, eigenvalue problems, eigenvalue algorithms, reduction to Hessenberg and tridiagonal forms, Rayleigh quotient and inverse iteration, QR algorithm, iterative methods, Arnoldi iteration, GMRES, Lanczos iteration, biorthogonalization methods, equilibrium and stiffness matrices, least squares for rectangular matrices, numerical differentiation using finite differences, numerical integration, and numerical solution of ordinary differential equations.

Textbooks: Trefethen, Lloyd N., and David Bau III., Numerical Linear Algebra, SIAM, 1997;
Strang, Gilbert. Computational Science and Engineering, Wellesley-Cambridge Press, 2007.

Topics: Discretization techniques, finite differences, implicit and explicit approaches, stability conditions, governing equations of fluid mechanics, conservative and primitive forms, closure, boundary conditions, well-posedness, strong conservation form, numerical solutions of compressible and incompressible Navier-Stokes equations, finite volume methods on structured and unstructured grids, pressure correction, SIMPLE algorithm, turbulence modeling, Reynolds-averaged and filtered Navier-Stokes equations, eddy viscosity, subgrid-scale models.

Textbook: Computational Fluid Dynamics: The Basics with Applications, 1st Edition, J. D. Anderson, ISBN-13: 978-0070016859, ISBN-10: 0070016852