The objective of this course is to introduce the students to the Finite Element Method for solving problems in the fields of Fluid Dynamics and Transport Phenomena.

Overview of the Transport Phenomena equations.

Overview of the Finite Element Method in one dimension: Weak form – Construction and assembly of local matrices – Application of Boundary Conditions – Convection and diffusion with the finite elements – Solution of time dependent problems. Finite element code development. Numerical integration – Gauss integration – Accuracy and stability of the finite element method. Petrov‐Galerkin method. Stabilization of convection terms.

Finite elements in two dimensions: Weak form of the differential equation. Construction of the 2‐d basis functions. Transformation from local to global representation – Application of boundary conditions. Solution of non‐linear problems with iterative methods, e.g. Picard iterations, Newton‐Raphson.

Mesh generation techniques: Spine method and elliptic method. Solution of elliptic recirculation problems: Solution of Navier‐Stokes in two dimensions. Application on the solution of the transport equation, the cavity problem and the dynamic rise of a free surface into a pore due to capillary forces.

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.
• Donea, J., & A., Huerta. Finite element methods for flow problems. John Wiley & Sons, 2003.
• Zienkienwicz, O.C., & R. L., Taylor. The Finite Element Method, Volumes I, III. Butterworth, Heinemann, 2000.
• Gresho, P. M., & R. L., Sani. Incompressible Flow and the Finite Element Method, Volumes I and II. Willey, 1998.
• Prenter, P. M. Splines and Variational Methods. Wiley, 1989.

Related Academic Journals:

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

Greek

Lectures