Dimitris A. Goussis

Courses:

- Undergraduate:

Fluid Mechanics

Introduction: Fluid properties and
characteristics, Units, Continuum hypothesis. Kinematics: Velocity and
acceleration fields, System and control volume, Transport theorem of
Reynolds, Forces and deformation. Surface and body forces: Pressure
forces, Viscous forces, Stress tensor. Governing equations in integral
and differential form: Mass, momentum and energy equations. The
Navier-Stokes equations. Potential flow. Dimensional analysis and
similitude: Pi theorem, Non-dimensional numbers. Inviscid flow:
Circulation, vortices. Viscous flows: Boundary layers, Separation.
Turbulence: Turbulent stress, Boussinesq hypothesis, Governing
equations for mass and momentum transfer.

Computational Fluid Mechanics

Linear and non-linear systems of
algebraic equations: direct and iterative algorithms. Systems of
ordinary differential equations: initial and boundary value problems,
explicit and implicit algorithms, multistep methods, stability,
convergence. Systems of partial differential equations: algorithms for
hyperbolic, parabolic and elliptic equations. Finite difference
methods: convection and diffusion operators, stability and convergence.
Algorithms for the solution of mass conservation and Navier-Stokes
equations.

Mathematical foundations. Analysis of stresses. Deformation and strain. Motion and flow; velocity, acceleration, vorticity. Fundamental laws of continuum mechanics; mass, momentum, energy. Fluids; steady, potential, viscous flows.

Continuum Mechanics

Mathematical foundations. Analysis of stresses. Deformation and strain. Motion and flow; velocity, acceleration, vorticity. Fundamental laws of continuum mechanics; mass, momentum, energy. Fluids; steady, potential, viscous flows.

- Graduate:

Fluid Mechanics (Program in Applied Mechanics)

Introduction: Continuum hypothesis,
System and Control Volume, Intensive and Extensive Properties,
Newtonian and non-Newtonian Fluids. Diffusive processes: Newton's Law,
Fourier's Law, Fick's Law. Elements of Tensor Analysis. Euler
and Lagrange derivatives. Methods for describing flow fields. Governing
equations in integral
and differential form: Mass, momentum and energy equations. Dimensional
analysis and
similitude. Turbulence: Closure, k-ε model, Reynolds Stress model, LES
model, PDF models. Heat and Mass Transfer: governing equations.
Constitutive for multi-component fluids. Chemical Kinetics. Examples.

Boundary Layer Behavior, Steady BLs (spatial multiscale): 2-point BV problem, Time dependent BLs (temporal multiscale): O'Malley-Vasil'eva expansion, Evolution equations: (temporal and spatial multiscale), Averaging, WKB methods, Algorithmic asymptotic methods.

Nonlinear Dynamics - Multiscale Analysis (Program in Computational Mechanics)

Boundary Layer Behavior, Steady BLs (spatial multiscale): 2-point BV problem, Time dependent BLs (temporal multiscale): O'Malley-Vasil'eva expansion, Evolution equations: (temporal and spatial multiscale), Averaging, WKB methods, Algorithmic asymptotic methods.