The goal of this course is to introduce the student into the fundamentals of numerical solution of Partial Differential Equations that model simple physical processes such convection, viscous dissipation and diffusion from the fields of Fluid Dynamics and Transport Phenomena, in one and two dimensional steady state and transient problems.

• Derivation of the fundamental conservation equations in differential form – Classification of Partial Differential Equations (PDE’s) in Elliptic Parabolic and Hyperbolic form
• Method of finite differences for the discretization and solution of PDE’s – Derivation of first and second modified PDE’s ‐ Accuracy stability and convergence of finite difference schemes – von Neuman Stability Analysis – Application in the 1‐d wave equation, i.e. the 1‐d convection equation
• Solution of parabolic problems with the finite difference method – Explicit and implicit time integration schemes for the solution of transient and steady state problems – Method of lines approach (Adams Bashforth‐Moulton and Runge‐Kutta methods ‐ Application to the solution of the transport equation that contains convection diffusion and production terms
• Solution of elliptic problems with the finite difference method ‐ Solution via direct matrix inversion (Gauss elimination vs LU decomposition) – Banded matrix inversion and the Thomas algorithm – Inversion using iterative and relaxation methods – Application in the calculation of the conduction shape factor in steady two dimensional heat transfer problems
• Application on the numerical solution of the non-linear Navier-Stokes equations for flow in an expansion, a cavity etc.
• Solution of hyperbolic problems with finite differences – Method of characteristics and the Riemann Invariants – Presentation of Finite difference schemes and their relative merits for the solution of the linear 2d wave equation – Contrast with algorithms for elliptic problems – Application on the solution of compressible potential flow around a thin object

Suggested Literature :

•  Asimakopoulos, D., & N., Markatos. Computational Fluid Dynamics. Papasotiriou, 1995. (in Greek).
• Bergeles, G. Computational Fluid Dynamics, Vol. 1 & 2, Symeon, 1997. (in Greek).
• Anderson, D.A., J. C., Tannehill & R. H., Pletcher. Numerical Heat Transfer & Fluid Flow. Taylor & Francis, 1997.
• Reddy, J. N. An Introduction to the Finite Element Method, McGraw Hill., 1993.
• Zikanov, O., Essential Computational Fluid Dynamics, John Wiley & Sons, Inc. USA, 2010.

Related Academic Journals:

• Journal of Fluid Mechanics
• Journal of Computational Fluids
• Physics of fluids
• Journal of Computational Physics

There are no prerequisite courses. It is recommended that students who are
interested in attending the course have completed successfully the following
courses:

ΓΕ1200 COMPUTER PROGRAMMING

ΓΕ0104 PARTIAL DIFFERENTIAL EQUATIONS

ΓΕ0105 NUMERICAL METHODS

ΕΝ0201 FLUID MECHANICS I

ΕΝ0202 FLUID MECHANICS II

ΕΝ0301 HEAT TRANSFER

Greek

Lectures and Laboratory Exercises