Dimitris A. Goussis

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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.
Sample Exam

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.

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.

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.